One mole of an ideal gas at 350 K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0 L to 3.0 L . The

Question

One mole of an ideal gas at 350 K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0 L to 3.0 L . The magnitude in change in entropy of the surroundings ( Δ S ) is ____ J K − 1 (Nearest integer) Given : R = 8.314 J K − 1 Mol − 1 .

TestHub · Accepted Answer

For an isothermal reversible expansion, $Δ S_{sys t e m} = n R ln (\frac{V _{2}}{V _{1}})$ .

$Δ S_{sys t e m} = 1 \times 8.314 \times ln (\frac{3.0}{2.0}) = 8.314 \times ln (1.5) = 8.314 \times 0.40546 = 3.37 J K^{- 1}$ .

For a reversible process, $Δ S_{t o t a l} = Δ S_{sys t e m} + Δ S_{s u rro u n d in g s} = 0$ .

Thus, $Δ S_{s u rro u n d in g s} = - Δ S_{sys t e m} = - 3.37 J K^{- 1}$ .

The magnitude is $3.37 J K^{- 1}$ , which is 3 (nearest integer).

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