Question

A gas which occupies a volume of 0.2 m³ at a pressure of 1 bar is expanded to a final pressure of 7.0 bar. The pressure of the gas varies according to the relation P = 1200 V + b. where P is in kPa, V is in m³ and b is a constant. Calculate the work done by the gas.

Answer 1

Given:

Volume occupied by gas = 0.2 m3

Pressure of gas = 1 bar = 100 kPa

The pressure volume relation is given by:

P = 1200 V + b

Substituting the values of P and V in the above equation:

100 = 1200 X 0.2 + b

100 = 240 + b

which gives :

b = -140 kPa

Therefore; the pressure volume relation becomes:

P = 1200 V - 140

Pressure after expansion = 7 bar = 700 kPa

Now; we calculate the volume after expansion.

700 = 1200 V - 140

1200 V = 840

V = 840 / 1200 = 0.7 m3

The work done by the gas is given by:

substituting the value of P in the above integral we get:

which on integration gives:

we have :

V1 = 0.2 m3

V2 = 0.7 m3

Substituting this in the expression of work done:

which on solving gives:

W = - 16 kbar.m3

which is the required work done by the gas.