Air in a spring-loaded piston/cylinder setup has a pressure that is linear with volume, P = A + BV. With an initial state of P = 150 kPa, V = 1 L and a final state of 800 kPa, V = 1.5 L, it is similar to the setup in Problem 3.48. Find the work done by the air. 3.54 Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. How much work does it give out?

3.48) Work done by the air is 1.05 kJ

3.54) 4.12 kJ of work is given out

Explanation:

3.48) Work done (W) = P2V2 - P1V1

P1 is initial pressure of air = 150 kPa

V1 is initial volume of air = 1 L = 1/1000 = 0.001 m^3

P2 is final pressure of air = 800 kPa

V2 is final volume of air = 1.5 L = 1.5/1000 = 0.0015 m^3

W = (800×0.0015) - (150×0.001) = 1.2 - 0.15 = 1.05 kJ

3.54) For a polytropic process

W = (P1V1 - P2V2)/(n - 1)

P1 is initial pressure of helium = 125 kPa

V1 is initial volume of helium = 0.25 m^3

P2 is final pressure of helium = 100 kPa

n is polytropic exponent = 1.667

V2 is final volume of helium = V1(P1/P2)^(1/n) = 0.25(125/100)^(1/1.667) = 0.25(1.25)^0.5999 = 0.25(1.14) = 0.285 m^3

W = (125×0.25 - 100×0.285)/(1.667 - 1) = (31.25 - 28.5)/0.667 = 2.75/0.667 = 4.12 kJ

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