Air is contained in a vertical piston-cylinder assembly by a piston of mass 50 k

Question

Air is contained in a vertical piston-cylinder assembly by a piston of mass 50 kg and having a face area of 0.01 m2. The mass of the air is 5 g, and initially the air occupies a volume of 5 L. The atmosphere exerts a pressure of 100 kPa on the top of the piston. The volume of the air slowly decreases to 0.002 m3 in a quasi-equilibrium process as the specific internal energy of the air decreases by 260 kJ/kg. Neglecting friction between the piston and the cylinder wall, determine the heat transfer to the air in kJ.

Explanation / Answer

let Pin = interna pressure of the air = Patmo + F/A

where F = weight of the piston

so, Pin = 100 Kpa + 50 x 9.81/(0.01*1000) Kpa

= 100 + 49.05

= 149.05 Kpa

initial volume = V1 = 5L = 0.005 m^3

final volume V 2 = 0.002 m^3

so, work done by air = Pin.dV = Pin x (V2 -V1) = 149.05 x (0.002 - 0.005)

W = - 0.44715 KJ = - 447.15 J

now, U = - 260 KJ/ Kg x 0.005 Kg = - 1.3 KJ

so, Q = dU +W by 1st law

so, Q = - 1.3 - 0.44715 = - 1.74715 KJ

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