compression step. The following are the works performed by the ideal gas at each
step (a work done by the ideal gas expressed as a positive value and on the ideal gas
as a negative value):
Step 1 (see Sect. 1.8)
W 12 ¼
Z
V 2
V 1
pdV ¼ NRT A ln
V 2
V 1
During the isothermal process, there is no change in the internal energy of the
ideal gas, it follows from the first law, Eq. (22),
Q A Q 12 ¼ W 12
Step 2
From the first law, Eq. (22), the work performed in an adiabatic step is equal to the
change in internal energy (a case that W is directly related to change in property)
W 23 ¼ U 2 T A
ð ÞÀU 3 T B
ð Þ
From Eqs. (34) and (37),
W 23 ¼ Nc V T A À T B
ð
Þ¼
NR
k À 1
T A À T B
ð
Þ
Fig. 4.4 Carnot gas cycle: Step 1 ! 2 is isothermal expansion; Step 2 ! 3 is reversible
adiabatic expansion; Step 3 ! 4 is isothermal compression; Step 4 ! 1 is reversible adiabatic
compression
4.5 Falling of Caloric in Reversible Processes
75