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Initially there are 3 [kg] of gas at a pressure of 200 [kPa] and specific volume of 1.5 [m3/kg] contained within a piston cylinder assembly. The gas undergoes a polytropic process for which P∀2=constant until the specific volume is 1.0 [m3/kg] and the specific internal energy decreases by 150 [kJ/kg]. Find the amount of heat transfer between the system and surroundings in [kJ].

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princessesther2011

Answer:

-900 kJ

Explanation:

Q = ∆U + W

The specific internal energy decreases by 150 kJ/kg, therefore, change in internal energy (∆U = -150 kJ/kg × 3 kg = -450 kJ)

W = (P2V2 - P1V1)/1-n

P2 = P1(V1/V2)^n

P1 = 200 kPa

V1 = 1.5 m^3/kg × 3 kg = 4.5 m^3

V2 = 1 m^3/kg × 3 kg = 3 m^3

n = 2

P2 = 200(4.5/3)^2 = 450 kPa

W = (450×3 - 200×4.5)/1-2 = -450 kJ

Q = -450 + (-450) = -450 - 450 = -900 kJ

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