specific heat capacity -- constant volume, constant pressure, which is greater?

[dessskris]

The specific heat capacity for the gas kept at constant volume is different to that when the gas is kept at constant pressure.

State and explain whether the specific heat capacity for an ideal gas at constant pressure is greater OR less than the specific heat capacity of the gas at constant volume.

[3 marks]

I do not know why if it is the work done, yes when the pressure is constant, the work done is greater than that when the volume is constant, because

δW = P δV

when V is constant, δV would be zero. thus the work done is zero and when P is constant, the work done would be greater.

but then the specific heat capacity...?

c = Q / m ΔT

it has got nothing to do with P and V.

I do not know why then :/

can anybody tell me which is greater and explain why? thank you!

[tenaciousdan]

First law of thermodynamics.

Q = ΔU + W ( = mcΔT )

So c is larger when W>0. Constant pressure means W>0 and hence constant pressure leads to larger c.

[genepeer]

Haha, I just did the exact same question in the May 10 past paper.

At constant volume, all heat energy added will be used to raise the temperature as no work is done by the gas.

At constant pressure, some heat will be used to do work (not raise temp.) and the rest will be used to raise the temperature. Therefore we'll need more energy to raise the temperature by the same degree. Hence greater specific heat at constant pressure.