Question

Assertion: The specific heat of a gas is an adiabatic process is zero and in an isothermal process is infinite. Reason: Specific heat of a gas in directly proportional to change of heat in system and inversely proportional to change in temperature.

Suppose an amount of heat ΔQ supplied to a substance changes its temperature from T to T + ΔT. Heat capacity of a substance to be S = ΔQ/ΔT. We expect ΔQ and, therefore, heat capacity S to be proportional to the mass of the substance. Further, it could also depend on the temperature, i.e., a different amount of heat may be needed for a unit rise in temperature at different temperatures. To define a constant characteristic of the substance and independent of its amount, we divide S by the mass of the substance m in kg: s = S/m = (1/m) ΔQ/ΔT, s is known as the specific heat capacity of the substance. It depends on the nature of the substance and its temperature. The unit of specific heat capacity is J kg-1 K-1

The molecule of a monatomic gas has only three translational degrees of freedom. Thus, the average energy of a molecule at temperature T is (3/2) kB T. The total internal energy of a mole of such a gas is U= 3/2 RT, and Cv= 3/2 R. A diatomic molecule treated as a rigid rotator, like a dumbbell, has 5 degrees of freedom: 3 translational and 2 rotational. Using the law of equipartition of energy, the total internal energy of a mole of such a gas is U =5/2 RT, CV =5/2 R. A polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number (f) of vibrational modes. According to the law of equipartition of energy it is easily seen that one mole of such a gas has, CV = (3+f) R. Note: CP-CV=R is true for any ideal gas, whether mono, di or polyatomic. The ratio of specific heats γ = CP/CV

ASSERTION: Specific heat capacity of a body is always lesser than its heat capacity. REASON: Heat capacity is heat required to raise temperature of unit mass of substance by unity.