Calculate the final volume of one mole of an ideal gas initially at 0^oC and 1 atm pressure. If it absorbs 2000 cal of heat during reversible isothermal expansion.

The gas is in the standard temperature and pressure condition i.e. at S.T.P

Hence V₁ = 22.4 dm³ and V₂ have to be calculated.

As given expansion is isothermal and reversible therefore, ∆U = 0
We know that ∆U = q + w
But ∆U = 0
Hence q = – w = 2000 cal
= 2000 X 4.184 J = 8368 J

As work done in reversible isothermal expansion is given by:
w= -nRT ln (V₂/ V₁)

Therefore nRT ln (V₂/ V₁) = – w = 8368 J
(I mol) X (8.314 J K^– mol^–) X (273 K) ln (V₂/ 22.4 dm³) = 8368 J
V₂ = 242.50 dm³

Hence the final volume of one mole of an ideal gas initially at 0^oC and 1 atm pressure is equal to 242.50 dm³