Page 190 - Advanced thermodynamics for engineers

176 CHAPTER 8 EQUATIONS OF STATE

, then the
Show that if the specific heat at constant pressure at some datum pressure p 0 is c p 0
value of the specific heat at constant pressure at the state (T, p) is given by

¼<TAe AT ð2 ATÞ p p o :
c p c p 0
P8.8 How can the equation of state in the form of a relationship between pressure, volume and
temperature be used to extend limited data on the entropy of a substance.
A certain gas, A, has the equation of state

pv ¼<Tð1 þ apÞ;

where a is a function of temperature alone. Show that

ds 1 da
¼ < þ a þ T :
dp p dT
T
Another gas B behaves as an ideal gas. If the molar entropy of gas A is equal to that of gas B
when both are at pressure p 0 and the same temperature T, show that if the pressure is increased
to p with the temperature maintained constant at T the molar entropy of gas B exceeds that of
gas A by an amount

da

< p p 0 a þ T :
dT
P8.9 A gas has the equation of state

pv
¼ a bT;
<T

where a and b are constants. If the gas is compressed reversibly and isothermally at the
temperature T show that the compression will also be adiabatic if
0
a
0
T ¼ :
2b