Introduction to Thermodynamics and Statistical Physics phần 5 pdf

2.5. Processes in Ideal Gas

V

p

isobaric

isothermal

isentropic

isochoric

V

p

isobaric

isothermal

isentropic

isochoric

Fig. 2.2. Four processes for which dN = 0.

thermal equilibrium throughout the entire process. This can be achieved by

varying the external parameters at a rate that is sufficiently slow to allow the

system to remain very close to thermal equilibrium at any moment during

the process. The four example to be analyzed below are (see fig. 2.2):

• Isothermal process - temperature is constant

• Isobaric process - pressure is constant

• Isochoric process - volume is constant

• Isentropic process - entropy is constant

Note that in general, using the definition of the heat capacity at constant

volume given by Eq. (2.67) together with Eq. (1.87) one finds that

cV =

µ∂U

∂τ ¶

N,V

. (2.95)

Furthermore, as can be seen from Eq. (2.85), the energy U of an ideal gas

in the classical limit is independent on the volume V (it can be expressed as

a function of τ and N only). Thus we conclude that for processes for which

dN = 0 the change in energy dU can be expressed as

dU = cV dτ . (2.96)

Eyal Buks Thermodynamics and Statistical Physics 61