Editing Heat capacity (section)

==== Calculating ''C<sub>p</sub>'' and ''C<sub>V</sub>'' for an ideal gas ====

[[Mayer's relation]]:

<math display="block">C_p - C_V = nR.</math>
<math display="block">C_p/C_V = \gamma,</math>

where:

* <math>n</math> is the number of moles of the gas,
* <math>R</math> is the [[Gas constant|universal gas constant]],
* <math>\gamma</math> is the [[heat capacity ratio]] (which can be calculated by knowing the number of [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of the gas molecule).

Using the above two relations, the specific heats can be deduced as follows:

<math display="block">C_V = \frac{nR}{\gamma - 1},</math>
<math display="block">C_p = \gamma \frac{nR}{\gamma - 1}.</math>
Following from the [[equipartition of energy]], it is deduced that an ideal gas has the isochoric heat capacity

<math display="block">C_V = n R \frac{N_f}{2} = n R \frac{3 + N_i}{2}</math>

where <math>N_f</math> is the number of [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of each individual particle in the gas, and <math>N_i = N_f - 3</math> is the number of [[Degrees of freedom (physics and chemistry)#Thermodynamic degrees of freedom for gases|internal degrees of freedom]], where the number 3 comes from the three translational degrees of freedom (for a gas in 3D space). This means that a [[Monatomic gas|monoatomic ideal gas]] (with zero internal degrees of freedom) will have isochoric heat capacity <math>C_v = \frac{3nR}{2}</math>.