Heat Capacities of Ideal Gases

All gases behave as ideal gases under moderate conditions not too extreme. This means that all gases obey the ideal gas equation  
\[pV=nRT\]
  and that the kinetic energy of the molecules of a gas is on average - for a monatomic gas is  
\[\frac{3}{2}kT\]
. Neither of these equation mentions the mass of the gas atoms, implying the the specific heat capacities of all monatomic gases is the same.
The total internal energy of a mol of gas is then  
\[U=N_A \times \frac{3}{2}kT= \frac{3}{2}RT\]
  where  
\[k, \; N_A, \; R\]
  are Boltzmann's, Avagadro's and the Gas Constant respectively. Hence the molar heat capacity - required to raise the temperature by 1 Degree - of all monatomic gases are the same, and this is true for any set of ideal gases with the same physical characteristics. The same is true of  
\[C_P\]
  - as implied by the relationship  
\[C_P=C_V+R\]
.
Not the the specific heat capacity is not the same as the molar heat capacity. In fact is  
\[m_R\]
  is the mass of one mol in kg then the number of mols in a kg is  
\[\frac{1}{m_R}\]
  and the specific heat capacity at constant volume will be  
\[\frac{C_V}{m_R}\]
.

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