A mass of gas at an initial pressure of 28 bar and with aninternel energy of 150

Question

A mass of gas at an initial pressure of 28 bar and with aninternel energy of 15000 kj is contained in well insulated cylinderof volume 0.06 m3 .the gas is allowed to expand behind apiston untill its interne energy is 1400 kj the law of expansion isPV2=constant calculute

i)the work done

ii)the final volume

iii)the final pressure A mass of gas at an initial pressure of 28 bar and with aninternel energy of 15000 kj is contained in well insulated cylinderof volume 0.06 m3 .the gas is allowed to expand behind apiston untill its interne energy is 1400 kj the law of expansion isPV2=constant calculute i)the work done ii)the final volume iii)the final pressure

Explanation / Answer

Given, P1=28 bar, V1=0.06 m3, U1=15000 kJ, U2=1400kJ 1-2 process is PV2=constant now, a) as the wall of cylinder is well insulated, Q of theprocess is zero. so applying first law of thermodynamics,U+W =Q or, (1400-15000) + W = 0 or, W = 13600 kJ or, work done by the gas =13600 kJ b)PV2 = constant or, (nRT/V)V2 = constant or, TV = constant or, T1V1 = T2V2 or, V2/V1= T1/T2 now, as internal energy is given by U = nCvT so, U1/U2 = T1/T2using this, V2/V1 = U1/U2 = 15000/1400 = 10.71 or, V2 = 10.71*0.06 = 0.64 m3 c)PV2 = constant or, P1V12 = P2V22 or, P2/P1= (V1/V2)2 = (1400/15000)2 or, P2 = 0.00871*28 = 0.2439 bar

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