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(B) When an ideal gas expands into a vacuum,the process is known as free expansion.Since the external pressure $P_{ext} = 0$,the work done $w = -P_{ex

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$\Delta S = nR \ln \frac{V_2}{V_1}$

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(B) When an ideal gas expands into a vacuum,the process is known as free expansion.Since the external pressure $P_{ext} = 0$,the work done $w = -P_{ext} \Delta V = 0$.For an ideal gas,internal energy depends only on temperature,so $\Delta U = 0$.According to the first law of thermodynamics,$\Delta U = q + w$,which implies $q = 0$.Since the process is adiabatic $(q = 0)$ and involves no work $(w = 0)$,the change in entropy for an ideal gas during isothermal expansion is given by $\Delta S = nR \ln \frac{V_2}{V_1}$.

What is the change in entropy when an ideal gas expands into a vacuum?

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