Question

A piston-cylinder device initially contains 0.4 m³ of air (to be treated as an ideal gas) at 100 kPa and 80°C. The air is now isothermally compressed to 0.1 m³. The work done during this process is ___________ kJ.

(Take the sign convention such that work done on the system is negative)

Answer 1

Concept:

Process → Isothermal i.e. constant temperature throughout

Work done during isothermal process, W

\(\Rightarrow W = {P_1}{V_1}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = {P_1}{V_1}\ln \left( {\frac{{{P_1}}}{{{P_2}}}} \right)\)

\(or\;W = {P_2}{V_2}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = {P_2}{V_2}\ln \left( {\frac{{{P_1}}}{{{P_2}}}} \right)\)

Here, V₁ = 0.4 m³, P₁ = 100 kPa, V₂ = 0.1 m³

\(W = {P_1}{V_1}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)\)

\(= 100 \times 0.4\ln \left( {\frac{{0.1}}{{0.4}}} \right)\)

⇒ W = -55.45 kJ