Question

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. neglecting changes in kinetic and potential energies determine the nonflow work in kJ.

Answer 1

The polytropic process is one in which the pressure-volume relation is given as $pV^n=constant$

$pV^{1.25} =constant\implies p_1V_1^{1.25}=p_2V_2^{1.25}$

$V_2=V_1(\frac{p_1}{p_2})^{\frac{1}{1.25}}=0.03(\frac{3500}{8500})^{\frac{1}{1.25}}=0.01475 m^3$

The work done during the polytropic process is found by substituting the pressure volume

relation into the boundary work equation. The result is $W= \int_1^2pdV=\frac{p_2V_2-p_1V_1}{1-n}$

$W=\frac{8500×10^3×0.01475-3500×10^3×0.03}{1-1.25}=-81500 J$

Then, according to the first law of thermodynamics, $ΔU=Q-W=-2500+81500=79000 J=79kJ$