A gas is compressed in a pistoncylinder assembly from p1 2

A gas is compressed in a piston-cylinder assembly from p_1 = 2 bar to p_2 = 8 bar, V_2 = 0.02 m^3 in a polytropic process during which the relationship between pressure and volume is pV^1.3 = constant. The mass of the gas is 0.5 kg. If the specific internal energy of the gas increases by 65 kJ/kg during the process, determine the heat transfer, in kJ. You may neglect changes in KE and PE for the system.

Solution

Given

P1 = 2 bar

P2 = 8 bar

V2 = 0.02 m3

dE = 65 KJ/ kg

m = 0.5 kg

n = 1.3 (power of V)

Solution

As process is polytropic ------- P1V1^1.3 = P2V2^1.3

V1 = ( P2/P1) ^1/1.3  V2 = ( 8/2) ^1/1.3  0.02 = 0.058 m3

V1 = 0.058 m3

Work done = W = (P2V2 - P1V1) /(1-n) = ( 800 x 0.02 - 200 x 0.058) / (1-1.3) = -14.66 KJ

Given dE = 65 KJ/ Kg ---------- = 65 x m = 65 x 0.5 = 32.5 KJ

As per 1 Law of thermodynamics

Q = dE + W = 32.5 -14.66 = 17.84 KJ

ANS = Q = 17.84 KJ