Question #137270

A piston cylinder contains gas initially at 3500 kPa with a volume of 0.03 cubic meter. The gas is compressed during a process where pV raise to 1.25 = C to a pressure of 8500 kPa. The heat transfer from the gas is 2.5 kJ. Determine the nonflow work in kj, neglecting changes in kinetic and potential energies.

Expert's answer

Initial pressure(p_{1})=3500x10^{3 }Pa

Initial Volume (V_{1})=0.03 m^{3}

Final pressure(p_{2})=8500 x10^{3 }Pa

Gas undergoes a polytropic process given by pV^{1.25}=constant

Therefore, for process 1-2 we can write,

"p_1 \\times {V_1}^{1.25} = p_2 \\times {V_2}^{1.25}"

"{V_2}^{1.25} =\\frac { p_1 \\times {V_1}^{1.25} }{p_2}" =0.01475 m^{3}

The work done during poly tropic process is given by

"W=\\frac {p_1 \\times V_1-p_2 \\times V_2}{n-1}"

"W=\\frac {(3500 \\times (0.03)-(8500)\\times (0.01475)}{1.25-1}" =-81.5 kJ (-ve sign indicates work done on the gas)

Work done on the gas is W=81.5 kJ

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