Which is the correct expression that relates change in entropy with the change in pressure for an ideal gas at constant temperature?

△ S = n R T l n \frac{P_{1}}{P_{2}}

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△ S = T (P_{2} - P_{1})

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△ S = n R l n (\frac{P_{1}}{P_{2}})

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△ S = R T l n (\frac{P_{1}}{P_{2}})

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Solution

The correct option is C $△ S = n R l n (\frac{P_{1}}{P_{2}})$
We know that entropy change in an isothermal process for an ideal gas is given as:
$△ S = n R l n (\frac{V_{2}}{V_{1}})$

Since $P_{1} V_{1} = P_{2} V_{2}$ according to Boyle's law at constant temperature we can also write,
$△ S = n R l n (\frac{P_{1}}{P_{2}})$

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