A polytropic process for an ideal gas in one in which pressure and volume are re
ID: 1900063 • Letter: A
Question
A polytropic process for an ideal gas in one in which pressure and volume are related by = const., where n is a constant. It is a generalization of the special processes considered earlier. Thus n = 0 defines an isobaric process, n = cp/cv an adiabatic process, n = 1 an isothermal process, and n = 8 an isochoric process. Suppose 1 kg of dry air at 280 K and 100 kPa undergoes a polytropic expansion in which the pressure falls to 70kPa and the potential temperature increases by 10 K. Solve for(a) the value of n;
(b) the change in internal energy of the air;
(c) the work done by the air;
(d) the heat absorbed by the air.
Explanation / Answer
PVn=constant
i.e P1-nTn=constant
so PTn/1-n =constant
100*280n/1-n=70*290n/1-n
n/1-n log280/290 =log0.7
n=10.16-10.16n
n=10.16/11.16 =0.91
b)change in internal energy=1000/28 *Cp*10=535.71 J
c)work done=change in internal eneergy
d)heat absorbed=0 as adiabatic process
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