A system has an initial volume of 10 ft3 and expands to a final volume of 20 ft3

Question

A system has an initial volume of 10 ft3 and expands to a final volume of 20 ft3. The initial pressure is 14.7 psi. Find the work done if the system is at the initial temperature of 75o F and the pressure between the final state is (a) constant, (b) inversely proportional to volume and (c) given by the ideal gas relationship (PV=mRT)
Answers: (a) 21,200 ft-lbf, (b)14,700 ft-lbf, (c) 14,700 ft-lbf

The answers were provided by the instructor but it does not help me understand how to solve. I would really appreciate the help. Thank you.

Explanation / Answer

2122 lb/ft2 = 14.7 psi a) W = P x change in volume = 2122x(20-10) = 21220 ft-lbf = 21200 (approx) b) W = integral (k dV /V) = k ln v2/v1 k =P1V1 = 2122 x 10 = 21220 so W = 21220 x ln 20/10 = 14708.58317 ft-lbf = 14700 (approx) c) same as 2 as mRT = P1V1= k = constant pls see for the approximations in conversion rate 2122 lb/ft2 = 14.7 psi

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