# Relationship between specific heat and volume

### Relations between heat capacities - Wikipedia inverse correlation between a solid's density and its specific heat. The quantitative relationship between heat transfer and temperature change Except for gases, the temperature and volume dependence of the specific heat of . Cp - the specific heat capacity at constant pressure conductivity, k (W/mK), and specific (volume) heat capacity, C (J/m^3K), through the following relationship.

In the United States other units of measure for heat capacity may be quoted in disciplines such as constructioncivil engineeringand chemical engineering. A still common system is the English Engineering Units in which the mass reference is pound mass and the temperature is specified in degrees Fahrenheit or Rankine.

One rare unit of heat is the pound calorie lb-caldefined as the amount of heat required to raise the temperature of one pound of water by one degree Celsius. More common is the British thermal unitthe standard unit of heat in the U. The path integral Monte Carlo method is a numerical approach for determining the values of heat capacity, based on quantum dynamical principles. However, good approximations can be made for gases in many states using simpler methods outlined below. Low temperature approximations for both gases and solids at temperatures less than their characteristic Einstein temperatures or Debye temperatures can be made by the methods of Einstein and Debye discussed below.

Most published data are given for standard pressure.

### Volumetric heat capacity - Wikipedia

However, different standard conditions for temperature and pressure have been defined by different organizations. This works reasonably well for many solids. For precise measurements, especially for gases, other aspects of measurement become critical. The heat capacity can be affected by many of the state variables that describe the thermodynamic system under study.

These include the starting and ending temperature, as well as the pressure and the volume of the system before and after heat is added. There is some difference in the heat capacity of monatomic vs. Volumetric heat capacities in polyatomic gases vary widely, however, since they are dependent largely on the number of atoms per molecule in the gas, which in turn determines the total number of atoms per volume in the gas.

In solids[ edit ] Since the bulk density of a solid chemical element is strongly related to its molar mass usually about 3 R per mole, as noted abovethere exists noticeable inverse correlation between a solid's density and its specific heat capacity on a per-mass basis. This is due to a very approximate tendency of atoms of most elements to be about the same size, despite much wider variations in density and atomic weight.

These two factors constancy of atomic volume and constancy of mole-specific heat capacity result in a good correlation between the volume of any given solid chemical element and its total heat capacity.

Another way of stating this, is that the volume-specific heat capacity volumetric heat capacity of solid elements is roughly a constant.

## Heat capacity

The molar volume of solid elements is very roughly constant, and even more reliably so also is the molar heat capacity for most solid substances. These two factors determine the volumetric heat capacity, which as a bulk property may be striking in consistency. Since the volume-specific corollary of the Dulong-Petit specific heat capacity relationship requires that atoms of all elements take up on average the same volume in solids, there are many departures from it, with most of these due to variations in atomic size.

For instance, arsenicwhich is only The heat capacity ratios of the two substances closely follows the ratios of their molar volumes the ratios of numbers of atoms in the same volume of each substance ; the departure from the correlation to simple volumes in this case is due to lighter arsenic atoms being significantly more closely packed than antimony atoms, instead of similar size.