Volumetric heat capacity
Overview

Volumetric heat capacity (VHC), also termed volume-specific heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

, describes the ability of a given volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

of a substance to store internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

while undergoing a given temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

change, but without undergoing a phase change. It is different from specific heat capacity in that the VHC depends on the volume of the material, while the specific heat is based on the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

of the material. If given a specific heat value of a substance, one can convert it to the VHC by multiply
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....

ing the specific heat by the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the substance.

Dulong
Pierre Louis Dulong
Pierre Louis Dulong was a French physicist and chemist, remembered today largely for the law of Dulong and Petit. He worked on the specific heat capacity and the expansion and refractive indices of gases....

and Petit
Alexis Thérèse Petit
Alexis Thérèse Petit was a French physicist. Petit is known for his work on the efficiencies of air- and steam-engines, published in 1818...

predicted in 1818 that ρcp would be constant for all solids.
Encyclopedia
Volumetric heat capacity (VHC), also termed volume-specific heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

, describes the ability of a given volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

of a substance to store internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

while undergoing a given temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

change, but without undergoing a phase change. It is different from specific heat capacity in that the VHC depends on the volume of the material, while the specific heat is based on the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

of the material. If given a specific heat value of a substance, one can convert it to the VHC by multiply
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....

ing the specific heat by the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the substance.

Dulong
Pierre Louis Dulong
Pierre Louis Dulong was a French physicist and chemist, remembered today largely for the law of Dulong and Petit. He worked on the specific heat capacity and the expansion and refractive indices of gases....

and Petit
Alexis Thérèse Petit
Alexis Thérèse Petit was a French physicist. Petit is known for his work on the efficiencies of air- and steam-engines, published in 1818...

predicted in 1818 that ρcp would be constant for all solids. In 1819 they found that the most constant quantity was the heat capacity of solids adjusted by the presumed weight of the atoms of the substance, as defined by Dalton (the Dulong-Petit law). This is the heat capacity per atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

, which suggests that it is the heat capacity per atom which is closest to being a constant in solids. The heat capacity on a volumetric basis actually varies from about 1.2 to 4.5 MJ/m³K, mostly due to differences in the physical size of atoms (if all atoms were the same size, the two kinds of heat capacity would be equivalent). For liquids, the volumetric heat capacity is in the range 1.3 to 1.9 MJ/m³K.

For monatomic gases (like argon) at room temperature and constant volume, it is about 0.5 kJ/m³K. The much lower value for gases results mostly from the fact that gases under standard conditions consist of mostly empty space (about 99.9% of volume), which is not filled by the atomic volumes of the atoms in the gas. This results in a factor of about 1000 loss in volumetric heat capacity. Monatomic gas heat capacities per atom are also additionally decreased by a factor of two with regard to solids, due to loss of half of the potential degrees of freedom
Degrees of freedom
Degrees of freedom can mean:* Degrees of freedom , independent displacements and/or rotations that specify the orientation of the body or system...

per atom for storing energy in a monatomic gas, as compared with regard to an ideal solid. There is some difference in the heat capacity of monatomic vs. polyatomic gasses, and also gas heat capacity is temperature-dependent in many ranges for polyatomic gases; these factors act to modestly (up to the discussed factor of two) increase heat capacity per atom in polyatomic gases.

The volumetric heat capacity is defined as having SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units of J
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

/(
Cubic metre
The cubic metre is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère...

·K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

). It can also be described in Imperial units of BTU
British thermal unit
The British thermal unit is a traditional unit of energy equal to about 1055 joules. It is approximately the amount of energy needed to heat of water, which is exactly one tenth of a UK gallon or about 0.1198 US gallons, from 39°F to 40°F...

/(ft³
Cubic foot
The cubic foot is an Imperial and US customary unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length.-Conversions:- Symbols :...

·
Fahrenheit
Fahrenheit is the temperature scale proposed in 1724 by, and named after, the German physicist Daniel Gabriel Fahrenheit . Within this scale, the freezing of water into ice is defined at 32 degrees, while the boiling point of water is defined to be 212 degrees...

).

## Thermal inertia

Thermal inertia is a term commonly used by scientist
Scientist
A scientist in a broad sense is one engaging in a systematic activity to acquire knowledge. In a more restricted sense, a scientist is an individual who uses the scientific method. The person may be an expert in one or more areas of science. This article focuses on the more restricted use of the word...

s and engineers modelling heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

s and is a bulk material property related to thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

and volumetric heat capacity. For example, this material has a high thermal inertia, or thermal inertia plays an important role in this system, which means that dynamic effects are prevalent in a model, so that a steady-state calculation will yield inaccurate results.

The term is a scientific analogy, and is not directly related to the mass-and-velocity term used in mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

, where inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...

is that which limits the acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

of an object. In a similar way, thermal inertia is a measure of the thermal mass and the velocity of the thermal wave which controls the surface temperature of a material. In heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

, a higher value of the volumetric heat capacity means a longer time for the system to reach equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

.

The thermal inertia of a material is defined as the square root of the product of the material's bulk thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

and volumetric heat capacity, where the latter is the product of density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

and specific heat capacity:

SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units of thermal inertia are J·m−2·K−1·s−1/2, also occasionally referred to as Kieffers, or more rarely, tiu.

For planetary surface materials, thermal inertia is the key property controlling the diurnal and seasonal surface temperature variations and is typically dependent on the physical properties of near-surface geologic materials. In remote sensing
Remote sensing
Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals Remote sensing...

applications, thermal inertia represents a complex combination of particle size, rock abundance, bedrock outcropping and the degree of induration. A rough approximation to thermal inertia is sometimes obtained from the amplitude of the diurnal temperature curve (i.e., maximum minus minimum surface temperature). The temperature of a material with low thermal inertia changes significantly during the day, while the temperature of a material with high thermal inertia does not change as drastically.
Deriving and understanding the thermal inertia of the surface can help to recognize small-scale features of that surface. In conjunction with other data, thermal inertia can help to characterize surface materials and the geologic processes responsible for forming these materials.

Thermal inertia of the oceans is a major factor influencing climate commitment, the degree of global warming
Global warming
Global warming refers to the rising average temperature of Earth's atmosphere and oceans and its projected continuation. In the last 100 years, Earth's average surface temperature increased by about with about two thirds of the increase occurring over just the last three decades...

predicted to eventually result from a step change in climate forcing such as a fixed increase in the atmospheric concentration of a greenhouse gas
Greenhouse gas
A greenhouse gas is a gas in an atmosphere that absorbs and emits radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The primary greenhouse gases in the Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone...

.

## Constant volume and constant pressure

For gases it is useful to distinguish between volumetric heat capacity at constant volume and at constant pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

. This distinction has the same meaning as for specific heat capacity.

• Heat Capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...

• Specific Heat Capacity
• Temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

• Thermal effusivity
• Thermodynamic equations
Thermodynamic equations
Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process...