Question

Calculate the work done in a reversible isothermal expansion of an ideal gas

Answer 1

Work done in reversible isothermal expansion can be given by-

W = - nRT ln (V₂/V₁)

• Reversible meaning the process is done infinitely so that the particle reverse from the final state exactly regenerates the initial state.
• Isothermal meaning temperature is constant throughout the whole process.
• Expansion is simply the increase in volume.

For an ideal gas first law of thermodynamics is

ΔU = q rev + W rev = 0

So,

W rev = - ∫ P dV = -q rev

W rev = - ∫ P .dV ( limits are from V₁ to V₂)

W rev = - nRT ln (V₂/V₁)