Choose the correct option for change in the entropy of the system ( Δ S sys ) | TestHub

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The second law of thermodynamics is a fundamental law of science. In this problem we consider the thermodynamics of an ideal gas, phase transition and chemical equilibrium. 3.00 mol of $CO_{2}$ gas expands isothermally (in thermal contact with the surroundings; temperature $= 15. 0^{\circ} C$ ) against a fixed external pressure of 1.00 bar. The initial and final volumes of the gas are 10.0 L and 30.0 L , respectively.

Choose the correct option for change in the entropy of the system $(Δ S_{sys})$ and of the surroundings $(Δ S_{sur})$ :

Options:

Answer:

C

Solution:

For an ideal gas undergoing **isothermal expansion**:

$Δ S_{sys} = n R ln \frac{V _{2}}{V _{1}}$

Since $V_{2} > V_{1}$ ,

$Δ S_{sys} > 0$

The gas expands against constant external pressure, so work is done by the system. Heat is absorbed from the surroundings to maintain a constant temperature; therefore:

$Δ S_{s u r} = \frac{q _{s u r}}{T} < 0$

Hence, the entropy of the system increases, and the entropy of the surroundings decreases.

Stream:JEESubject:ChemistryTopic:Thermodynamics - IISubtopic:Miscellaneous/Mixed

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Chemistry - Thermodynamics - II Question with Solution | TestHub

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