diff --git a/modules/doc/content/newsletter/2024/2024_09.md b/modules/doc/content/newsletter/2024/2024_09.md
index 1169934a8f36..64efc847b999 100644
--- a/modules/doc/content/newsletter/2024/2024_09.md
+++ b/modules/doc/content/newsletter/2024/2024_09.md
@@ -7,6 +7,13 @@ for a complete description of all MOOSE changes.
 
 ## MOOSE Improvements
 
+### Specific internal energy added to Solid Properties objects
+
+The [ThermalSolidProperties.md] objects from the [Solid properties module](modules/solid_properties/index.md)
+now provide interfaces to compute the specific internal energy as a function of
+temperature. This new interface is useful, for example, in measuring the
+internal energy in solids for energy conservation verification.
+
 ## libMesh-level Changes
 
 ## PETSc-level Changes
diff --git a/modules/solid_properties/doc/content/modules/solid_properties/index.md b/modules/solid_properties/doc/content/modules/solid_properties/index.md
index ee61b3c638f8..e6b750015ffc 100644
--- a/modules/solid_properties/doc/content/modules/solid_properties/index.md
+++ b/modules/solid_properties/doc/content/modules/solid_properties/index.md
@@ -63,17 +63,19 @@ Userobjects available in the Solid Properties module that provide thermal proper
 An example will be provided later on this page for creating a new solid userobject.
 
 On their own, these userobjects do not execute; their functions must be called from other
-objects. The most common use case is to compute material properties with these
-userobjects, which can be accomplished with
-[ThermalSolidPropertiesMaterial](/materials/ThermalSolidPropertiesMaterial.md);
-its `computeQpProperties` method evaluates the thermal conductivity, isobaric specific heat, and density at
-the quadrature points using the values of a coupled variable representing temperature
-plus the functions provided by the selected userobject:
-
-!listing modules/solid_properties/src/materials/ThermalSolidPropertiesMaterial.C start=computeQpProperties
-
-Another use case is to get a single property into a post-processor,
-which is accomplished with [ThermalSolidPropertiesPostprocessor.md].
+objects. Some potentially useful classes that call them are:
+
+- [ThermalSolidPropertiesFunctorMaterial.md]: A functor material that declares
+  functor material properties for density, thermal conductivity, isobaric specific heat,
+  and specific internal energy. An option is provided for using a constant density.
+  This functor material can have its functor material properties converted to
+  regular AD or non-AD material properties by using it in conjunction with
+  [(AD)MaterialFunctorConverter](MaterialFunctorConverter.md).
+- [ThermalSolidPropertiesMaterial.md] and [ConstantDensityThermalSolidPropertiesMaterial.md],
+  which declare AD or non-AD material properties for density, thermal conductivity, and isobaric specific heat,
+  using variable density and constant density, respectively.
+- [ThermalSolidPropertiesPostprocessor.md] evaluates density, thermal conductivity,
+  or isobaric specific heat at a single temperature value.
 
 ## Usage
 
diff --git a/modules/solid_properties/doc/content/source/functormaterials/ThermalSolidPropertiesFunctorMaterial.md b/modules/solid_properties/doc/content/source/functormaterials/ThermalSolidPropertiesFunctorMaterial.md
index 5957060ad60a..1ca3e401f3ee 100644
--- a/modules/solid_properties/doc/content/source/functormaterials/ThermalSolidPropertiesFunctorMaterial.md
+++ b/modules/solid_properties/doc/content/source/functormaterials/ThermalSolidPropertiesFunctorMaterial.md
@@ -2,17 +2,14 @@
 
 ## Description
 
-The `ThermalSolidPropertiesFunctorMaterial` material declares
-density, specific heat, and thermal
-conductivity as functor material properties. They are evaluated on-the-fly
-on every query.
+`ThermalSolidPropertiesFunctorMaterial` declares functor material properties for
+density, specific heat, and thermal conductivity, and specific internal energy.
 
-!alert warning title=Conservation on fixed-sized domains
-Using a variable density can lead to mass/energy conservation errors if using
-a fixed-size domain. If this is a concern, it is recommended to use
-a constant density, specified independently using a [GenericFunctorMaterial.md] for example.
-For the density parameter of `ThermalSolidPropertiesFunctorMaterial` you may then use a
-placeholder dummy name.
+The parameter [!param](/FunctorMaterials/ThermalSolidPropertiesFunctorMaterial/use_constant_density)
+can be used to specify that the density should be constant, evaluated at the temperature
+[!param](/FunctorMaterials/ThermalSolidPropertiesFunctorMaterial/T_ref). This is
+useful because for fixed-sized domains, mass/energy conservation errors result
+from using a variable density.
 
 !syntax parameters /FunctorMaterials/ThermalSolidPropertiesFunctorMaterial
 
diff --git a/modules/solid_properties/doc/content/source/solidproperties/ThermalSolidProperties.md b/modules/solid_properties/doc/content/source/solidproperties/ThermalSolidProperties.md
index aef4cad16bc5..b681525f4a9c 100644
--- a/modules/solid_properties/doc/content/source/solidproperties/ThermalSolidProperties.md
+++ b/modules/solid_properties/doc/content/source/solidproperties/ThermalSolidProperties.md
@@ -2,21 +2,68 @@
 
 This is the base class for providing thermal solid properties
 as a function of temperature.
-This class defines functions to compute the following thermal properties
-as a function of temperature:
+This class defines functions to compute the following thermal properties,
+which are all assumed to be functions of temperature only:
 
-- compute isobaric specific heat - `Real cp_from_T(const Real & T)`
-- compute thermal conductivity - `Real k_from_T(const Real & T)`
-- compute density - `Real rho_from_T(const Real & T)`
+- `cp`: isobaric specific heat, $c_p$
+- `e`: specific internal energy, $e$
+- `k`: thermal conductivity, $k$
+- `rho`: density, $\rho$
 
-Functions to compute derivatives of these properties as a function of temperature
-are also available:
+For each of these, the following methods are available, where `y` should be
+replaced by the respective property name given in the list above:
 
-- compute isobaric specific heat and its temperature derivative - `void cp_from_T(const Real & T, Real & cp, Real & dcp_dT)`
-- compute thermal conductivity and its temperature derivative - `void k_from_T(const Real & T, Real & k, Real & dk_dT)`
-- compute density and its temperature derivative - `void rho_from_T(const Real & T, Real & rho, Real & drho_dT)`
+```
+Real y_from_T(const Real & T) const
+```
 
-To create a new userobject providing thermal properties, derive from this
-userobject and specify implementations of the above functions.
+provides the value $y(T)$ using a `Real` input value for $T$.
+
+```
+void y_from_T(const Real & T, Real & y, Real & dy_dT) const
+```
+
+provides the value $y(T)$ and its derivative $y'(T)$ using a `Real` input value for $T$.
+
+```
+ADReal y_from_T(const ADReal & T) const
+```
+
+provides the value $y(T)$ and its derivative $y'(T)$ using an `ADReal` input value for $T$.
+
+Thus both AD and non-AD interfaces are available. Derived classes are only responsible
+for overriding the non-AD interfaces for each property. The AD interfaces are
+implemented by default by combining the two non-AD interfaces.
+
+Note that the `e_from_T` interfaces should not be overridden because they have
+generic implementations, and the non-AD interfaces are not even virtual.
+Instead, derived classes must override the following:
+
+```
+Real cp_integral(const Real & T) const
+```
+
+which corresponds to the indefinite integral $C(T)$ of $c_p(T)$, minus the
+constant of integration:
+
+!equation
+C(T) = \int c_p(T) dT \,.
+
+Due to the definition of the isobaric specific heat capacity,
+
+!equation
+c_p \equiv \left.\frac{\partial e}{\partial T}\right|_v \,,
+
+the specific internal energy can be expressed as
+
+!equation
+e(T) - e(T_0) = \int\limits_{T_0}^T c_p(T') dT' = C(T) - C(T_0) \,,
+
+where $T_0$ is the temperature at which the specific internal energy is assumed
+to be zero. This is a convention supplied by the user using the parameter
+[!param](/SolidProperties/ThermalSS316Properties/T_zero_e). By default, this
+is taken to be at standard temperature, 273.15 K. Note that this is important
+for comparing specific internal energy values to external sources, which may
+be based on different reference temperatures.
 
 !bibtex bibliography
diff --git a/modules/solid_properties/include/base/SolidPropertiesNames.h b/modules/solid_properties/include/base/SolidPropertiesNames.h
index 4f79d0ba0b99..9fb59167f723 100644
--- a/modules/solid_properties/include/base/SolidPropertiesNames.h
+++ b/modules/solid_properties/include/base/SolidPropertiesNames.h
@@ -16,4 +16,5 @@ namespace SolidPropertiesNames
 static const std::string thermal_conductivity = "thermal_conductivity";
 static const std::string density = "density";
 static const std::string specific_heat = "specific_heat";
+static const std::string specific_internal_energy = "specific_internal_energy";
 }
diff --git a/modules/solid_properties/include/solidproperties/ThermalCompositeSiCProperties.h b/modules/solid_properties/include/solidproperties/ThermalCompositeSiCProperties.h
index c6a673c5affc..daa137cb4b57 100644
--- a/modules/solid_properties/include/solidproperties/ThermalCompositeSiCProperties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalCompositeSiCProperties.h
@@ -32,6 +32,8 @@ class ThermalCompositeSiCProperties : public ThermalSolidProperties
 
   virtual void cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const override;
 
+  virtual Real cp_integral(const Real & T) const override;
+
   virtual Real rho_from_T(const Real & T) const override;
 
   virtual void rho_from_T(const Real & T, Real & rho, Real & drho_dT) const override;
@@ -39,6 +41,12 @@ class ThermalCompositeSiCProperties : public ThermalSolidProperties
 protected:
   /// (constant) density
   const Real & _rho_const;
+
+  // Constants used in specific heat relation
+  const Real _c1;
+  const Real _c2;
+  const Real _c3;
+  const Real _c4;
 };
 
 #pragma GCC diagnostic pop
diff --git a/modules/solid_properties/include/solidproperties/ThermalGraphiteProperties.h b/modules/solid_properties/include/solidproperties/ThermalGraphiteProperties.h
index 3cbf96f87b3f..c836f792b4b4 100644
--- a/modules/solid_properties/include/solidproperties/ThermalGraphiteProperties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalGraphiteProperties.h
@@ -32,6 +32,8 @@ class ThermalGraphiteProperties : public ThermalSolidProperties
 
   virtual void cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const override;
 
+  virtual Real cp_integral(const Real & T) const override;
+
   virtual Real rho_from_T(const Real & T) const override;
 
   virtual void rho_from_T(const Real & T, Real & rho, Real & drho_dT) const override;
@@ -45,6 +47,15 @@ class ThermalGraphiteProperties : public ThermalSolidProperties
 
   /// constant density
   const Real & _rho_const;
+
+  // Constants used in specific heat relation
+  const Real _c1;
+  const Real _c2;
+  const Real _c3;
+  const Real _c4;
+  const Real _c5;
+  const Real _c6;
+  const Real _c7;
 };
 
 #pragma GCC diagnostic pop
diff --git a/modules/solid_properties/include/solidproperties/ThermalMonolithicSiCProperties.h b/modules/solid_properties/include/solidproperties/ThermalMonolithicSiCProperties.h
index d6f46f497734..07f11e59eb15 100644
--- a/modules/solid_properties/include/solidproperties/ThermalMonolithicSiCProperties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalMonolithicSiCProperties.h
@@ -32,6 +32,8 @@ class ThermalMonolithicSiCProperties : public ThermalSolidProperties
 
   virtual void cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const override;
 
+  virtual Real cp_integral(const Real & T) const override;
+
   virtual Real rho_from_T(const Real & T) const override;
 
   virtual void rho_from_T(const Real & T, Real & rho, Real & drho_dT) const override;
@@ -46,6 +48,12 @@ class ThermalMonolithicSiCProperties : public ThermalSolidProperties
 
   /// (constant) density
   const Real & _rho_const;
+
+  // Constants used in specific heat relation
+  const Real _c1;
+  const Real _c2;
+  const Real _c3;
+  const Real _c4;
 };
 
 #pragma GCC diagnostic pop
diff --git a/modules/solid_properties/include/solidproperties/ThermalSS316Properties.h b/modules/solid_properties/include/solidproperties/ThermalSS316Properties.h
index 1b303d8c075c..b09898f9aff4 100644
--- a/modules/solid_properties/include/solidproperties/ThermalSS316Properties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalSS316Properties.h
@@ -33,9 +33,16 @@ class ThermalSS316Properties : public ThermalSolidProperties
 
   virtual void cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const override;
 
+  virtual Real cp_integral(const Real & T) const override;
+
   virtual Real rho_from_T(const Real & T) const override;
 
   virtual void rho_from_T(const Real & T, Real & rho, Real & drho_dT) const override;
+
+protected:
+  // Constants used in specific heat relation
+  const Real _c1;
+  const Real _c2;
 };
 
 #pragma GCC diagnostic pop
diff --git a/modules/solid_properties/include/solidproperties/ThermalSolidProperties.h b/modules/solid_properties/include/solidproperties/ThermalSolidProperties.h
index a869ddf3e336..979816eaaad4 100644
--- a/modules/solid_properties/include/solidproperties/ThermalSolidProperties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalSolidProperties.h
@@ -11,10 +11,31 @@
 
 #include "SolidProperties.h"
 
+/**
+ * Adds default error implementation for non-AD value, which should be overridden in child classes
+ */
+#define propfuncNonADValueOnly(want)                                                               \
+  virtual Real want##_from_T(const Real &) const                                                   \
+  {                                                                                                \
+    mooseError(__PRETTY_FUNCTION__, " not implemented.");                                          \
+  }
+
+/**
+ * Adds default error implementation for non-AD value and derivatives, which should be overridden
+ * in child classes
+ */
+#define propfuncNonADDerivatives(want)                                                             \
+  virtual void want##_from_T(const Real & T, Real & val, Real & d##want##dT) const                 \
+  {                                                                                                \
+    solidPropError(__PRETTY_FUNCTION__, " derivatives not implemented.");                          \
+    d##want##dT = 0;                                                                               \
+    val = want##_from_T(T);                                                                        \
+  }
+
 /**
  * Adds AD versions of each solid property. These functions use the Real versions of these methods
  * to compute the AD variables complete with derivatives. Typically, these do not need to be
- * overriden in derived classes.
+ * overridden in derived classes.
  */
 #define propfuncAD(want)                                                                           \
   virtual ADReal want##_from_T(const ADReal & T) const                                             \
@@ -27,26 +48,13 @@
     ADReal result = x;                                                                             \
     result.derivatives() = T.derivatives() * dxdT;                                                 \
     return result;                                                                                 \
-  }                                                                                                \
-                                                                                                   \
-/**                                                                                                \
- * Adds function definitions with not implemented error. These functions should be overriden in    \
- * derived classes where required. AD versions are constructed automatically using propfuncAD.     \
+  }
+
+/**
+ * Adds function definitions with not implemented error. These functions should be overridden in
+ * derived classes where required. AD versions are constructed automatically using propfuncAD.
  */
-#define propfunc(want)                                                                             \
-  virtual Real want##_from_T(const Real &) const                                                   \
-  {                                                                                                \
-    mooseError(__PRETTY_FUNCTION__, " not implemented.");                                          \
-  }                                                                                                \
-                                                                                                   \
-  virtual void want##_from_T(const Real & T, Real & val, Real & d##want##dT) const                 \
-  {                                                                                                \
-    solidPropError(__PRETTY_FUNCTION__, " derivatives not implemented.");                          \
-    d##want##dT = 0;                                                                               \
-    val = want##_from_T(T);                                                                        \
-  }                                                                                                \
-                                                                                                   \
-  propfuncAD(want)
+#define propfunc(want) propfuncNonADValueOnly(want) propfuncNonADDerivatives(want) propfuncAD(want)
 
 /**
  * Common class for solid properties that are a function of temperature
@@ -84,6 +92,24 @@ class ThermalSolidProperties : public SolidProperties
   propfunc(k)
   propfunc(cp)
   propfunc(rho)
+
+  /**
+   * Computes the integral of isobaric specific heat capacity w.r.t. temperature,
+   * from the zero-e reference temperature, provided by a user parameter.
+   *
+   * Note that the constant of integration is not included. This function is
+   * called in the \c e_from_T(T) method.
+   */
+  virtual Real cp_integral(const Real & /*T*/) const
+  {
+    mooseError(__PRETTY_FUNCTION__, " not implemented.");
+  }
+
+  // Specific internal energy methods; these designed to not be virtual; only
+  // cp_integral(T) needs to be implemented.
+  Real e_from_T(const Real & T) const;
+  void e_from_T(const Real & T, Real & val, Real & dedT) const;
+  propfuncAD(e)
   ///@}
 
   // clang-format on
@@ -101,6 +127,10 @@ class ThermalSolidProperties : public SolidProperties
     else
       mooseError(std::forward<Args>(args)...);
   }
+
+protected:
+  /// Temperature at which the specific internal energy is assumed to be zero
+  const Real _T_zero_e;
 };
 
 #pragma GCC diagnostic pop
diff --git a/modules/solid_properties/include/solidproperties/ThermalUCProperties.h b/modules/solid_properties/include/solidproperties/ThermalUCProperties.h
index c2aab49774e4..7d6566d96a5f 100644
--- a/modules/solid_properties/include/solidproperties/ThermalUCProperties.h
+++ b/modules/solid_properties/include/solidproperties/ThermalUCProperties.h
@@ -26,6 +26,9 @@ class ThermalUCProperties : public ThermalSolidProperties
   virtual Real cp_from_T(const Real & T) const override;
   virtual void cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const override;
 
+  using ThermalSolidProperties::cp_integral;
+  virtual Real cp_integral(const Real & T) const override;
+
   using ThermalSolidProperties::rho_from_T;
   virtual Real rho_from_T(const Real & T) const override;
   virtual void rho_from_T(const Real & T, Real & rho, Real & drho_dT) const override;
@@ -33,4 +36,10 @@ class ThermalUCProperties : public ThermalSolidProperties
 protected:
   /// (constant) density
   const Real & _rho_const;
+
+  // Constants used in specific heat relation
+  const Real _c1;
+  const Real _c2;
+  const Real _c3;
+  const Real _c4;
 };
diff --git a/modules/solid_properties/src/functormaterials/ThermalSolidPropertiesFunctorMaterial.C b/modules/solid_properties/src/functormaterials/ThermalSolidPropertiesFunctorMaterial.C
index dfbf17a5d5dd..15bb218c330a 100644
--- a/modules/solid_properties/src/functormaterials/ThermalSolidPropertiesFunctorMaterial.C
+++ b/modules/solid_properties/src/functormaterials/ThermalSolidPropertiesFunctorMaterial.C
@@ -19,6 +19,10 @@ ThermalSolidPropertiesFunctorMaterial::validParams()
   InputParameters params = FunctorMaterial::validParams();
   params.addRequiredParam<MooseFunctorName>("temperature", "Temperature");
   params.addRequiredParam<UserObjectName>("sp", "The name of the user object for solid properties");
+  params.addParam<bool>("use_constant_density", false, "Use constant density evaluated at 'T_ref'");
+  params.addParam<Real>(
+      "T_ref",
+      "Temperature at which to evaluate density if 'use_constant_density' is set to 'true'");
   params.addParam<std::string>(SolidPropertiesNames::specific_heat,
                                SolidPropertiesNames::specific_heat,
                                "Name to be used for the isobaric specific heat");
@@ -28,6 +32,9 @@ ThermalSolidPropertiesFunctorMaterial::validParams()
   params.addParam<std::string>(SolidPropertiesNames::density,
                                SolidPropertiesNames::density,
                                "Name to be used for the density");
+  params.addParam<std::string>(SolidPropertiesNames::specific_internal_energy,
+                               SolidPropertiesNames::specific_internal_energy,
+                               "Name to be used for the specific internal energy");
   params.addClassDescription("Computes solid thermal properties as a function of temperature");
   return params;
 }
@@ -38,13 +45,38 @@ ThermalSolidPropertiesFunctorMaterial::ThermalSolidPropertiesFunctorMaterial(
     _temperature(getFunctor<ADReal>("temperature")),
     _sp(getUserObject<ThermalSolidProperties>("sp"))
 {
+  if (getParam<bool>("use_constant_density"))
+  {
+    if (isParamValid("T_ref"))
+    {
+      const Real T_ref = getParam<Real>("T_ref");
+      addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::density),
+                                 [this, T_ref](const auto & /*r*/, const auto & /*t*/) -> ADReal
+                                 { return _sp.rho_from_T(T_ref); });
+    }
+    else
+      paramError("T_ref",
+                 "The parameter 'T_ref' is required if 'use_constant_density' is set to 'true'.");
+  }
+  else
+  {
+    if (isParamValid("T_ref"))
+      paramError("T_ref",
+                 "The parameter 'T_ref' may not be specified if 'use_constant_density' is set to "
+                 "'false'.");
+    else
+      addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::density),
+                                 [this](const auto & r, const auto & t) -> ADReal
+                                 { return _sp.rho_from_T(_temperature(r, t)); });
+  }
+
   addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::specific_heat),
                              [this](const auto & r, const auto & t) -> ADReal
                              { return _sp.cp_from_T(_temperature(r, t)); });
   addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::thermal_conductivity),
                              [this](const auto & r, const auto & t) -> ADReal
                              { return _sp.k_from_T(_temperature(r, t)); });
-  addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::density),
+  addFunctorProperty<ADReal>(getParam<std::string>(SolidPropertiesNames::specific_internal_energy),
                              [this](const auto & r, const auto & t) -> ADReal
-                             { return _sp.rho_from_T(_temperature(r, t)); });
+                             { return _sp.e_from_T(_temperature(r, t)); });
 }
diff --git a/modules/solid_properties/src/solidproperties/ThermalCompositeSiCProperties.C b/modules/solid_properties/src/solidproperties/ThermalCompositeSiCProperties.C
index 0dc30ddbbebc..6350193ef014 100644
--- a/modules/solid_properties/src/solidproperties/ThermalCompositeSiCProperties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalCompositeSiCProperties.C
@@ -23,21 +23,32 @@ ThermalCompositeSiCProperties::validParams()
 }
 
 ThermalCompositeSiCProperties::ThermalCompositeSiCProperties(const InputParameters & parameters)
-  : ThermalSolidProperties(parameters), _rho_const(getParam<Real>("density"))
+  : ThermalSolidProperties(parameters),
+    _rho_const(getParam<Real>("density")),
+    _c1(925.65),
+    _c2(0.3772),
+    _c3(7.9259e-5),
+    _c4(3.1946e7)
 {
 }
 
 Real
 ThermalCompositeSiCProperties::cp_from_T(const Real & T) const
 {
-  return 925.65 + 0.3772 * T - 7.9259e-5 * Utility::pow<2>(T) - 3.1946e7 / Utility::pow<2>(T);
+  return _c1 + _c2 * T - _c3 * Utility::pow<2>(T) - _c4 / Utility::pow<2>(T);
 }
 
 void
 ThermalCompositeSiCProperties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const
 {
   cp = cp_from_T(T);
-  dcp_dT = 0.3772 - 1.58518e-4 * T + 6.3892e7 / Utility::pow<3>(T);
+  dcp_dT = _c2 - 2.0 * _c3 * T + 2.0 * _c4 / Utility::pow<3>(T);
+}
+
+Real
+ThermalCompositeSiCProperties::cp_integral(const Real & T) const
+{
+  return _c1 * T + 0.5 * _c2 * Utility::pow<2>(T) - _c3 / 3.0 * Utility::pow<3>(T) + _c4 / T;
 }
 
 Real
diff --git a/modules/solid_properties/src/solidproperties/ThermalGraphiteProperties.C b/modules/solid_properties/src/solidproperties/ThermalGraphiteProperties.C
index c5d0d3213c2a..8dc7feb11637 100644
--- a/modules/solid_properties/src/solidproperties/ThermalGraphiteProperties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalGraphiteProperties.C
@@ -27,7 +27,14 @@ ThermalGraphiteProperties::validParams()
 ThermalGraphiteProperties::ThermalGraphiteProperties(const InputParameters & parameters)
   : ThermalSolidProperties(parameters),
     _grade(getParam<MooseEnum>("grade").getEnum<GraphiteGrade>()),
-    _rho_const(getParam<Real>("density"))
+    _rho_const(getParam<Real>("density")),
+    _c1(4184.0),
+    _c2(0.54212),
+    _c3(2.42667e-6),
+    _c4(90.2725),
+    _c5(43449.3),
+    _c6(1.59309e7),
+    _c7(1.43688e9)
 {
 }
 
@@ -37,8 +44,8 @@ ThermalGraphiteProperties::cp_from_T(const Real & T) const
   switch (_grade)
   {
     case GraphiteGrade::H_451:
-      return 4184.0 * (0.54212 - 2.42667e-6 * T - 90.2725 / T - 43449.3 / Utility::pow<2>(T) +
-                       1.59309e7 / Utility::pow<3>(T) - 1.43688e9 / Utility::pow<4>(T));
+      return _c1 * (_c2 - _c3 * T - _c4 / T - _c5 / Utility::pow<2>(T) + _c6 / Utility::pow<3>(T) -
+                    _c7 / Utility::pow<4>(T));
     default:
       mooseError("Unhandled GraphiteGrade enum!");
   }
@@ -53,8 +60,8 @@ ThermalGraphiteProperties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) c
   {
     case GraphiteGrade::H_451:
     {
-      dcp_dT = 4184.0 * (-2.42667e-6 + 90.2725 / Utility::pow<2>(T) + 86898.6 / Utility::pow<3>(T) -
-                         4.77927e7 / Utility::pow<4>(T) + 5.74752e9 / Utility::pow<5>(T));
+      dcp_dT = _c1 * (-_c3 + _c4 / Utility::pow<2>(T) + 2.0 * _c5 / Utility::pow<3>(T) -
+                      3.0 * _c6 / Utility::pow<4>(T) + 4.0 * _c7 / Utility::pow<5>(T));
       break;
     }
     default:
@@ -62,6 +69,21 @@ ThermalGraphiteProperties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) c
   }
 }
 
+Real
+ThermalGraphiteProperties::cp_integral(const Real & T) const
+{
+  switch (_grade)
+  {
+    case GraphiteGrade::H_451:
+    {
+      return _c1 * (_c2 * T - 0.5 * _c3 * Utility::pow<2>(T) - _c4 * std::log(T) + _c5 / T -
+                    0.5 * _c6 / Utility::pow<2>(T) + _c7 / (3.0 * Utility::pow<3>(T)));
+    }
+    default:
+      mooseError("Unhandled GraphiteGrade enum!");
+  }
+}
+
 Real
 ThermalGraphiteProperties::k_from_T(const Real & T) const
 {
diff --git a/modules/solid_properties/src/solidproperties/ThermalMonolithicSiCProperties.C b/modules/solid_properties/src/solidproperties/ThermalMonolithicSiCProperties.C
index f185d0fa9cae..39819003ada9 100644
--- a/modules/solid_properties/src/solidproperties/ThermalMonolithicSiCProperties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalMonolithicSiCProperties.C
@@ -29,21 +29,31 @@ ThermalMonolithicSiCProperties::validParams()
 ThermalMonolithicSiCProperties::ThermalMonolithicSiCProperties(const InputParameters & parameters)
   : ThermalSolidProperties(parameters),
     _k_model(getParam<MooseEnum>("thermal_conductivity_model").getEnum<ThermalConductivityModel>()),
-    _rho_const(getParam<Real>("density"))
+    _rho_const(getParam<Real>("density")),
+    _c1(925.65),
+    _c2(0.3772),
+    _c3(7.9259e-5),
+    _c4(3.1946e7)
 {
 }
 
 Real
 ThermalMonolithicSiCProperties::cp_from_T(const Real & T) const
 {
-  return 925.65 + 0.3772 * T - 7.9259e-5 * Utility::pow<2>(T) - 3.1946e7 / Utility::pow<2>(T);
+  return _c1 + _c2 * T - _c3 * Utility::pow<2>(T) - _c4 / Utility::pow<2>(T);
 }
 
 void
 ThermalMonolithicSiCProperties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const
 {
   cp = cp_from_T(T);
-  dcp_dT = 0.3772 - 1.58518e-4 * T + 6.3892e7 / Utility::pow<3>(T);
+  dcp_dT = _c2 - 2 * _c3 * T + 2 * _c4 / Utility::pow<3>(T);
+}
+
+Real
+ThermalMonolithicSiCProperties::cp_integral(const Real & T) const
+{
+  return _c1 * T + 0.5 * _c2 * Utility::pow<2>(T) - _c3 / 3.0 * Utility::pow<3>(T) + _c4 / T;
 }
 
 Real
diff --git a/modules/solid_properties/src/solidproperties/ThermalSS316Properties.C b/modules/solid_properties/src/solidproperties/ThermalSS316Properties.C
index caf8e3b0dea0..063e61b59b4c 100644
--- a/modules/solid_properties/src/solidproperties/ThermalSS316Properties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalSS316Properties.C
@@ -21,21 +21,27 @@ ThermalSS316Properties::validParams()
 }
 
 ThermalSS316Properties::ThermalSS316Properties(const InputParameters & parameters)
-  : ThermalSolidProperties(parameters)
+  : ThermalSolidProperties(parameters), _c1(0.1816), _c2(428.46)
 {
 }
 
 Real
 ThermalSS316Properties::cp_from_T(const Real & T) const
 {
-  return 0.1816 * T + 428.46;
+  return _c1 * T + _c2;
 }
 
 void
 ThermalSS316Properties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const
 {
   cp = cp_from_T(T);
-  dcp_dT = 0.1816;
+  dcp_dT = _c1;
+}
+
+Real
+ThermalSS316Properties::cp_integral(const Real & T) const
+{
+  return 0.5 * _c1 * T * T + _c2 * T;
 }
 
 Real
diff --git a/modules/solid_properties/src/solidproperties/ThermalSolidProperties.C b/modules/solid_properties/src/solidproperties/ThermalSolidProperties.C
index b9202cb0938b..4cf1878055c3 100644
--- a/modules/solid_properties/src/solidproperties/ThermalSolidProperties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalSolidProperties.C
@@ -13,10 +13,30 @@ InputParameters
 ThermalSolidProperties::validParams()
 {
   InputParameters params = SolidProperties::validParams();
+
+  // There does not seem to be a conventional reference temperature, so STP was chosen.
+  params.addParam<Real>(
+      "T_zero_e",
+      273.15,
+      "Temperature at which the specific internal energy is assumed to be zero [K].");
+
   return params;
 }
 
 ThermalSolidProperties::ThermalSolidProperties(const InputParameters & parameters)
-  : SolidProperties(parameters)
+  : SolidProperties(parameters), _T_zero_e(getParam<Real>("T_zero_e"))
+{
+}
+
+Real
+ThermalSolidProperties::e_from_T(const Real & T) const
+{
+  return cp_integral(T) - cp_integral(_T_zero_e);
+}
+
+void
+ThermalSolidProperties::e_from_T(const Real & T, Real & e, Real & de_dT) const
 {
+  e = e_from_T(T);
+  de_dT = cp_from_T(T);
 }
diff --git a/modules/solid_properties/src/solidproperties/ThermalUCProperties.C b/modules/solid_properties/src/solidproperties/ThermalUCProperties.C
index 2b40bb025155..a6214b9d9964 100644
--- a/modules/solid_properties/src/solidproperties/ThermalUCProperties.C
+++ b/modules/solid_properties/src/solidproperties/ThermalUCProperties.C
@@ -24,7 +24,12 @@ ThermalUCProperties::validParams()
 }
 
 ThermalUCProperties::ThermalUCProperties(const InputParameters & parameters)
-  : ThermalSolidProperties(parameters), _rho_const(getParam<Real>("density"))
+  : ThermalSolidProperties(parameters),
+    _rho_const(getParam<Real>("density")),
+    _c1(239.7),
+    _c2(5.068e-3),
+    _c3(1.7604e-5),
+    _c4(3488100)
 {
 }
 
@@ -34,7 +39,7 @@ ThermalUCProperties::cp_from_T(const Real & T) const
   if ((T < 298) || (T > 2838))
     flagInvalidSolution(
         "UC specific heat evaluated outside of UC cp temperature range [298, 2838] K");
-  return 239.7 - 5.068e-3 * T + 1.7604e-5 * Utility::pow<2>(T) - 3488100 / Utility::pow<2>(T);
+  return _c1 - _c2 * T + _c3 * Utility::pow<2>(T) - _c4 / Utility::pow<2>(T);
 }
 
 void
@@ -46,7 +51,13 @@ ThermalUCProperties::cp_from_T(const Real & T, Real & cp, Real & dcp_dT) const
         "UC specific heat evaluated outside of UC cp temperature range [298, 2838] K");
 
   cp = cp_from_T(T);
-  dcp_dT = -5.068e-3 + 3.5208e-5 * T + 6976200 / Utility::pow<3>(T);
+  dcp_dT = -_c2 + 2 * _c3 * T + 2 * _c4 / Utility::pow<3>(T);
+}
+
+Real
+ThermalUCProperties::cp_integral(const Real & T) const
+{
+  return _c1 * T - 0.5 * _c2 * Utility::pow<2>(T) + _c3 / 3.0 * Utility::pow<3>(T) + _c4 / T;
 }
 
 Real
diff --git a/modules/solid_properties/test/include/utils/SolidPropertiesTestUtils.h b/modules/solid_properties/test/include/utils/SolidPropertiesTestUtils.h
index 9f2e29cc1d38..74196ce30cf3 100644
--- a/modules/solid_properties/test/include/utils/SolidPropertiesTestUtils.h
+++ b/modules/solid_properties/test/include/utils/SolidPropertiesTestUtils.h
@@ -55,3 +55,15 @@
   {                                                                                                \
     DERIV_TEST_CUSTOM_PERTURBATION(f, a, tol, REL_PERTURBATION);                                   \
   }
+
+// Macro for testing that the definition of the derivative of specific internal energy is
+// consistent with the definition of the isobaric specific heat capacity
+#define SPECIFIC_INTERNAL_ENERGY_TESTS(sp, T, dT, rel_tol)                                         \
+  {                                                                                                \
+    const Real de_dT_fd = (sp->e_from_T(T + dT) - sp->e_from_T(T - dT)) / (2 * dT);                \
+    Real e, de_dT;                                                                                 \
+    sp->e_from_T(T, e, de_dT);                                                                     \
+    REL_TEST(e, sp->e_from_T(T), REL_TOL_CONSISTENCY);                                             \
+    REL_TEST(de_dT, de_dT_fd, rel_tol);                                                            \
+    REL_TEST(sp->cp_from_T(T), de_dT, rel_tol);                                                    \
+  }
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/test.i b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/base.i
similarity index 76%
rename from modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/test.i
rename to modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/base.i
index d0ac3c7a6b55..67f7d99cc0ca 100644
--- a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/test.i
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/base.i
@@ -18,7 +18,7 @@ T_initial = 300
   []
 []
 
-[Materials]
+[FunctorMaterials]
   [sp_mat]
     type = ThermalSolidPropertiesFunctorMaterial
     temperature = T
@@ -26,6 +26,7 @@ T_initial = 300
     specific_heat = cp
     density = rho
     thermal_conductivity = k
+    specific_internal_energy = e
   []
 []
 
@@ -46,17 +47,21 @@ T_initial = 300
 
 [Postprocessors]
   [cp]
-    type = ElementIntegralFunctorPostprocessor
+    type = ElementExtremeFunctorValue
     functor = 'cp'
   []
   [k]
-    type = ElementIntegralFunctorPostprocessor
+    type = ElementExtremeFunctorValue
     functor = 'k'
   []
   [density]
-    type = ElementIntegralFunctorPostprocessor
+    type = ElementExtremeFunctorValue
     functor = 'rho'
   []
+  [e]
+    type = ElementExtremeFunctorValue
+    functor = 'e'
+  []
 []
 
 [Problem]
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/constant_density.i b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/constant_density.i
new file mode 100644
index 000000000000..509cfea1a58a
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/constant_density.i
@@ -0,0 +1,12 @@
+!include base.i
+
+[FunctorMaterials]
+  [sp_mat]
+    use_constant_density = True
+    T_ref = 500
+  []
+[]
+
+[Outputs]
+  file_base = constant_density
+[]
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_no_T_ref.i b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_no_T_ref.i
new file mode 100644
index 000000000000..99aca34f4a41
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_no_T_ref.i
@@ -0,0 +1,7 @@
+!include base.i
+
+[FunctorMaterials]
+  [sp_mat]
+    use_constant_density = True
+  []
+[]
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_provided_T_ref.i b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_provided_T_ref.i
new file mode 100644
index 000000000000..e7b876a38c70
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/error_provided_T_ref.i
@@ -0,0 +1,7 @@
+!include base.i
+
+[FunctorMaterials]
+  [sp_mat]
+    T_ref = 500
+  []
+[]
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/constant_density.csv b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/constant_density.csv
new file mode 100644
index 000000000000..a758559a6161
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/constant_density.csv
@@ -0,0 +1,2 @@
+time,cp,density,e,k
+0,482.94,7863.415,12901.479237,13.79891
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/test_out.csv b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/test_out.csv
deleted file mode 100644
index bacea3c59fb1..000000000000
--- a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/test_out.csv
+++ /dev/null
@@ -1,2 +0,0 @@
-time,cp,density,k
-0,482.94,7956.4814,13.79891
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/variable_density.csv b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/variable_density.csv
new file mode 100644
index 000000000000..47ece37e8da9
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/gold/variable_density.csv
@@ -0,0 +1,2 @@
+time,cp,density,e,k
+0,482.94,7956.4814,12901.479237,13.79891
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/tests b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/tests
index 3e54bce5d69b..213c8a0a6f28 100644
--- a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/tests
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/tests
@@ -1,11 +1,31 @@
 [Tests]
+  design = 'ThermalSolidPropertiesFunctorMaterial.md'
+  issues = '#21978'
   [test]
-    type = CSVDiff
-    input = 'test.i'
-    csvdiff = 'test_out.csv'
-    requirement = "The system shall provide the ability to use functors for solid material "
-                  "properties."
-    design = 'ThermalSolidPropertiesFunctorMaterial.md'
-    issues = '#21978'
+    requirement = "The system shall provide the ability to use functors for solid material properties"
+    [variable_density]
+      type = CSVDiff
+      input = 'variable_density.i'
+      csvdiff = 'variable_density.csv'
+      detail = "with a temperature-dependent density."
+    []
+    [constant_density]
+      type = CSVDiff
+      input = 'constant_density.i'
+      csvdiff = 'constant_density.csv'
+      detail = "with a constant density."
+    []
+    [error_no_T_ref]
+      type = RunException
+      input = 'error_no_T_ref.i'
+      expect_err = "The parameter 'T_ref' is required if 'use_constant_density' is set to 'true'"
+      detail = "and report an error if no reference temperature is supplied for a constant density."
+    []
+    [error_provided_T_ref]
+      type = RunException
+      input = 'error_provided_T_ref.i'
+      expect_err = "The parameter 'T_ref' may not be specified if 'use_constant_density' is set to 'false'"
+      detail = "and report an error if a reference temperature is supplied for a variable density."
+    []
   []
 []
diff --git a/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/variable_density.i b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/variable_density.i
new file mode 100644
index 000000000000..e4f7d14b36c9
--- /dev/null
+++ b/modules/solid_properties/test/tests/materials/thermal_solid_functor_properties/variable_density.i
@@ -0,0 +1,5 @@
+!include base.i
+
+[Outputs]
+  file_base = variable_density
+[]
diff --git a/modules/solid_properties/unit/src/ThermalCompositeSiCPropertiesTest.C b/modules/solid_properties/unit/src/ThermalCompositeSiCPropertiesTest.C
index 56ccba3cc724..cccc10bed764 100644
--- a/modules/solid_properties/unit/src/ThermalCompositeSiCPropertiesTest.C
+++ b/modules/solid_properties/unit/src/ThermalCompositeSiCPropertiesTest.C
@@ -44,6 +44,17 @@ TEST_F(ThermalCompositeSiCPropertiesTest, cp)
   DERIV_TEST(_sp1->cp_from_T, T, REL_TOL_DERIVATIVE);
 }
 
+/**
+ * Test that the specific internal energy and its derivatives are
+ * correctly computed.
+ */
+TEST_F(ThermalCompositeSiCPropertiesTest, e)
+{
+  const Real T = 800.0;
+  REL_TEST(_sp1->e_from_T(T), 504301.09074042423, REL_TOL_SAVED_VALUE);
+  SPECIFIC_INTERNAL_ENERGY_TESTS(_sp1, T, 1e-6, 1e-6);
+}
+
 /**
  * Test that the density and its derivatives are
  * correctly computed.
diff --git a/modules/solid_properties/unit/src/ThermalGraphitePropertiesTest.C b/modules/solid_properties/unit/src/ThermalGraphitePropertiesTest.C
index 8093368a1d8c..5af251c0b99d 100644
--- a/modules/solid_properties/unit/src/ThermalGraphitePropertiesTest.C
+++ b/modules/solid_properties/unit/src/ThermalGraphitePropertiesTest.C
@@ -44,6 +44,17 @@ TEST_F(ThermalGraphitePropertiesTest, cp)
   DERIV_TEST(_sp1->cp_from_T, T, REL_TOL_DERIVATIVE);
 }
 
+/**
+ * Test that the specific internal energy and its derivatives are
+ * correctly computed.
+ */
+TEST_F(ThermalGraphitePropertiesTest, e)
+{
+  const Real T = 800.0;
+  REL_TEST(_sp1->e_from_T(T), 648167.7112224712, REL_TOL_SAVED_VALUE);
+  SPECIFIC_INTERNAL_ENERGY_TESTS(_sp1, T, 1e-6, 1e-6);
+}
+
 /**
  * Test that the density and its derivatives are
  * correctly computed.
diff --git a/modules/solid_properties/unit/src/ThermalMonolithicSiCPropertiesTest.C b/modules/solid_properties/unit/src/ThermalMonolithicSiCPropertiesTest.C
index e3190d842c9e..626a2a9cff68 100644
--- a/modules/solid_properties/unit/src/ThermalMonolithicSiCPropertiesTest.C
+++ b/modules/solid_properties/unit/src/ThermalMonolithicSiCPropertiesTest.C
@@ -54,6 +54,17 @@ TEST_F(ThermalMonolithicSiCPropertiesTest, cp)
   DERIV_TEST(_sp1->cp_from_T, T, REL_TOL_DERIVATIVE);
 }
 
+/**
+ * Test that the specific internal energy and its derivatives are
+ * correctly computed.
+ */
+TEST_F(ThermalMonolithicSiCPropertiesTest, e)
+{
+  const Real T = 800.0;
+  REL_TEST(_sp1->e_from_T(T), 504301.09074042423, REL_TOL_SAVED_VALUE);
+  SPECIFIC_INTERNAL_ENERGY_TESTS(_sp1, T, 1e-6, 1e-6);
+}
+
 /**
  * Test that the density and its derivatives are
  * correctly computed.
diff --git a/modules/solid_properties/unit/src/ThermalSS316PropertiesTest.C b/modules/solid_properties/unit/src/ThermalSS316PropertiesTest.C
index 95bb84284107..193d563a974c 100644
--- a/modules/solid_properties/unit/src/ThermalSS316PropertiesTest.C
+++ b/modules/solid_properties/unit/src/ThermalSS316PropertiesTest.C
@@ -44,6 +44,17 @@ TEST_F(ThermalSS316PropertiesTest, cp)
   DERIV_TEST(_sp->cp_from_T, T, REL_TOL_DERIVATIVE);
 }
 
+/**
+ * Test that the specific internal energy and its derivatives are
+ * correctly computed.
+ */
+TEST_F(ThermalSS316PropertiesTest, e)
+{
+  const Real T = 800.0;
+  REL_TEST(_sp->e_from_T(T), 277071.479237, REL_TOL_SAVED_VALUE);
+  SPECIFIC_INTERNAL_ENERGY_TESTS(_sp, T, 1e-6, 1e-6);
+}
+
 /**
  * Test that the density and its derivatives are
  * correctly computed.
diff --git a/modules/solid_properties/unit/src/ThermalUCPropertiesTest.C b/modules/solid_properties/unit/src/ThermalUCPropertiesTest.C
index 851e745cd2b6..01201953d7b7 100644
--- a/modules/solid_properties/unit/src/ThermalUCPropertiesTest.C
+++ b/modules/solid_properties/unit/src/ThermalUCPropertiesTest.C
@@ -44,6 +44,17 @@ TEST_F(ThermalUCPropertiesTest, cp)
   DERIV_TEST(_sp1->cp_from_T, T, REL_TOL_DERIVATIVE);
 }
 
+/**
+ * Test that the specific internal energy and its derivatives are
+ * correctly computed.
+ */
+TEST_F(ThermalUCPropertiesTest, e)
+{
+  const Real T = 800.0;
+  REL_TEST(_sp1->e_from_T(T), 119328.29374852851, REL_TOL_SAVED_VALUE);
+  SPECIFIC_INTERNAL_ENERGY_TESTS(_sp1, T, 1e-6, 1e-6);
+}
+
 /**
  * Test that the density and its derivatives are
  * correctly computed.