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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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