During an expansion process, the pressure of a gas changes from 15 to 140 psia according to the relation P = aV + b, where a = 5 psia/ft3 and b is a constant. If the initial volume of the gas is 7 ft3, calculate the work done during the process.

The work done during the process is 359 btu

Explanation:

Given-

P1 = 15psia

P2 = 140 psia

V1 = 7ft³

a = 5 psia/ft³

b = C

P = aV + b

Work done, W = ?

P1 = aV1 + b

15 = 5 (7) + b

b = - 20 psia

P2 = aV2 + b

140 = 5 (V2) - 20

V2 = 32 ft³

The work done by the process is the area under the curve which is trapezoidal.

Therefore,

Work done, W = area of trapezoid

= (P2 + P1 / 2) (V2 - V1)

= (140 + 15 / 2) (32 - 7)

= 1937.5 psia ft³

= 1937.5 / 5.4039 = 359 btu

Therefore, the work done during the process is 359 btu