SPECIFIC HEAT AND MOLAR HEAT CAPACITY
(1) Specific heat (or specific heat capacity) of a substance is the quantity of heat (in calories, joules, kcal, or kilo joules) required to raise the temperature of 1g of that substance through 1oC. It can be measured at constant pressure (Cp) and at constant volume (Cv).
(2) Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1oC.
∴ Molar heat capacity = Specific heat capacity × Molecular weight, i.e., Cv = cv × M and Cp = cp × M.
(3) Since gases on heating show considerable tendency towards expansion if heated under constant pressure conditions, an additional energy has to be supplied for raising its temperature by 1oC relative to that required under constant volume conditions, i.e.,
Cp > Cv or Cp = Cv + Work done in expansion, PV (= R)
where, Cp = molar heat capacity at constant pressure
Cp = molar heat capacity at constant volume.
(4) Some useful relations of Cp and Cv
(i) Cp – Cv = R = 2 calories = 8.314 J
(ii) Cp = 3/2 R (for monoatomic gas) and Cv = 3/2 + x (for di and polyatomic gas), where x varies from gas to gas.
(iii) Cp/Cp = γ (Ratio of molar capacities)
(iv) For monoatomic gas, Cp = 3. calories whereas, Cp = Cv + R = 5 calories
(v) For monoatomic gas, (γ) = Cp/Cv = 5/2R/3/2R = 1.66
(vi) For diatomic gas (γ) = Cp/Cv = 7/2R/5/2R = 1.40
(vii) For triatomic gas (γ) = Cp/Cv = 8R/6R = 1.33
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