Answer:
The polytropic exponent (n) is 1.2
The amount of energy transfer by work is 552.45 Btu
Explanation:
P1V1^n = P2V2^n
P1 = 75 lbf/in^2 = 75 lbf/in^2 × 143.3 in^2/ft^2 = 10,747.5 lbf/ft^2
V1 = 4 ft^3/lb × 10 lb = 40 ft^3
P2 = 20 lbf/in^2 = 20 × 143.3 = 2866 lbf/ft^2
V2 = 12 ft^3/lb × 10 lb = 120 ft^3
(V2/V1)^n = P1/P2
(120/40)^n = 10747.5/2866
3^n = 3.75
ln 3^n = ln 3.75
n ln 3 = ln 3.75
n = ln 3.75/ln 3 = 1.2
W = (P2V2 - P1V1)/1 - n = (2866×120 - 10747.5×40)/1-1.2 = (343,920 - 429,900)/-0.2 = -85,980/-0.2 = 429,900 lbf.ft = 429,900/778.17 Btu = 552.45 Btu
