Specific and Molar heat capacity of the gases

         (1) Specific heat (or specific heat capacity) of a substance is the quantity of heat (in kcal, joules, calories, or kilo joules) needed to raise the temperature of 1g of that substance through 1^oC. It can be measured at constant pressure (C_p) and at constant volume (C_v).

         (2) The Molar heat capacity of the substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1 degree C.

   Molar heat capacity = Specific heat capacity * Molecular weight which gives

                        C_v = c_v * M and C_p = c_p * M.

         (3) As the gases upon heating show the considerable tendency towards expansion if heated under constant pressure conditions additionally the energy has to be supplied for raising its temperature by 1 degree C relative to that required under constant volume conditions which gives

         C_p>C_v or C_p = C_v + Work done on expansion, P V(=R)

         where, C_p molar heat capacity at constant pressure; C_v ^is molar heat capacity at constant volume.

         (4) Some useful relations of C_p and C_v

         (i)           C_p-C_v = R = 2 Calories = 8.314 J

         (ii)           (for mono atomic gas) and      (for di and polyatomic gas), where x varies from gas to gas.

         (iii)     (Ratio of molar capacities)

         (iv) For monoatomic gas C_v = 3 Calories whereas, C_p = C_v + R = 5 Calories

         (v)          For monoatomic gas,     .

         (vi) For diatomic gas 

         (vii) For triatomic gas 

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