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  
  and that the kinetic energy of the molecules of a gas is on average - for a monatomic gas is  
. 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  
\[U=N_A \times \frac{3}{2}kT= \frac{3}{2}RT\]
\[k, \; N_A, \; R\]
  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  
  - as implied by the relationship  
Not the the specific heat capacity is not the same as the molar heat capacity. In fact is  
  is the mass of one mol in kg then the number of mols in a kg is  
  and the specific heat capacity at constant volume will be  

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