Answer to Question #277747 in Mechanical Engineering for nav

Question

piston-cylinder contains gas initially at 3500 kPaa with a volume of 0.03 mº. The gas is compressed during a process where pV 1.25 C to a pressure of 8500 kPaa. The heat transfer from the gas is 2.5 kJ. Determine the change in internal energy, neglecting changes in kinetic and potential energies.

Answer 1

Initial pressure(p₁)=3500x10³ Pa

Initial Volume (V₁)=0.03 m³

Final pressure(p₂)=8500 x10³ Pa

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

Therefore, for process 1-2 we can write,

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

${V_2}^{1.25} =\frac { p_1 \times {V_1}^{1.25} }{p_2}$

The work done during poly tropic process is given by

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

$W=\frac {(3500 \times (0.03)-(8500)\times (0.01475)}{1.25-1}$

Work done on the gas is W=81.5 kJ

Δ𝑈= −2500+81500=79000𝐽=79𝑘𝐽