Final answer:
The molar specific heat at a constant volume of an ideal gas depends on the molecular structure of the gas, specifically the degrees of freedom of the molecules. Monatomic gases have a lower specific heat at constant volume compared to diatomic or polyatomic gases. This value, usually denoted as Cv, can be calculated using the gas constant R and considering the type of molecular motion present.
Step-by-step explanation:
The molar specific heat at a constant volume of an ideal gas depends on the degrees of freedom of the gas molecules. Specifically, for monatomic gases which have only translational motion, the molar specific heat at constant volume (Cv) is determined by the relationship Cv = (3/2)R, where R is the gas constant. For diatomic or polyatomic gases, the specific heat at constant volume also accounts for rotational and vibrational motions, leading to higher values of Cv compared to monatomic gases.
In general, specific heat capacities are empirical values that can be measured under controlled conditions and can vary with temperature and pressure. However, for the purpose of many calculations, these values are often treated as constants within a normal temperature range. This assumption is valid because the temperature and volume dependence of the specific heat for most substances, including gases, is relatively weak at normal temperatures. It's important to note, the heat capacity at constant volume is different from the heat capacity at constant pressure (Cp), and these two are related for an ideal gas by the equation Cp = Cv + R.