Thermal Physics - Specific Heat

For an ideal gas, the specific heat at constant pressure C_p is greater than the specific heat at constant volume C_v because the

1. Gas does work on its environment when its pressure remains constant while its temperature is increased.
2. Heat input per degree increase in temperature is the same in processes for which either the pressure or the volume is kept constant.
3. Pressure of the gas remains constant when its temperature remains constant.
4. Increase in the gas’s internal energy is greater when the pressure remains constant than when the volume remains constant
5. Heat needed is greater when the volume remains constant than when the pressure remains constant.

(GR8677 #14)

Solution:

(A) TRUE.
Heat Capacity: C = Q/dT

First law of Thermodynamics: the change in internal energy of a system dU is equal to the heat Q added and the work, W done on or by the system 
→ dU = Q ± W

W done on the system → +W
W done by the system → −W

Gas (the system) does work on its environment
W done by the system
dU = Q − W

At constant V:
Work, W = PdV = 0
Q = dU
C_v = dU/dT

At constant P:
Work, W = PdV ≠ 0
Q = dU + W
C_p = dU/dT + PdV/dT = C_v + PdV/dT
C_p  C_v

(B) FALSE.
This means C_p = C_v, but according to A, C_p  C_v

(C) FALSE.
Ideal gas law: PV = NkT
If T constant, P changes if V changes.

(D) FALSE.
Heat Capacity, C = Q/dT does not depend on the gas’ internal energy, U

(E) FALSE.
See A. At constant V, Q = dU.
At constant P, Q = dU + W.

Answer: A