# An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If ${T}_{i}$ , is the initial temperature and ${T}_{f}$ is the final temperature, which of the following statements is correct?

1. A

${T}_{\mathrm{f}}={T}_{\mathrm{i}}$ for both reversible and irreversible processes

2. B

${\left({T}_{\mathrm{f}}\right)}_{\mathrm{irrev}}>{\left({T}_{\mathrm{f}}\right)}_{\mathrm{rev}}$

3. C

${T}_{\mathrm{f}}>{T}_{\mathrm{i}}$ for reversible processes but ${T}_{\mathrm{f}}={T}_{\mathrm{i}}$ for irreversible processes

4. D

${\left({T}_{\mathrm{f}}\right)}_{\mathrm{irrev}}={\left({T}_{\mathrm{f}}\right)}_{\mathrm{rev}}$

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### Solution:

An ideal gas does more work in reversible expansion as compared to irreversible expansion. Since the expansion is carried out in an isolated system (adiabatic conditions), the decrease in the internal energy will be larger under reversible conditions and hence it involves larger decrease in temperature leading to the fact ${\left({T}_{\mathrm{f}}\right)}_{\mathrm{irrv}}>{\left({T}_{\mathrm{f}}\right)}_{\mathrm{rev}}$

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