CBSE-XI-Physics
27: Specific Heat Capacities of Gases
- #1Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CA and CB be the molar heat capacities for the two processes,
(a) CA = CB
(b) CA < CB
(c) CA > CB
(d) CA and CB cannot be defined.digAnsr: cAns : (c) CA > CB
According to the first law of thermodynamics, `` \,\mathrm{\,\Delta \,}Q=\,\mathrm{\,\Delta \,}U+\,\mathrm{\,\Delta \,}W``, where `` ∆``Q is the heat supplied to the system when `` \Delta ``W work is done on the system and `` ∆``U is the change in internal energy produced. Since the temperature rises by the same amount in both processes, change in internal energies are same, i.e. `` ∆``UA = `` ∆``UB.
But as, `` ∆``WA = `` ∆``WB this gives `` \Delta ``QA = 2`` \Delta ``QB.
Now, molar heat capacity of a gas, `` C=\frac{\,\mathrm{\,\Delta \,}Q}{n\,\mathrm{\,\Delta \,}T}``, where `` ∆``Q/n is the heat supplied to a mole of gas and `` ∆``T is the change in temperature produced. As `` ∆``QA = 2`` ∆``QB, CA > CB.
Page No 76: