Two gases have the same initial pressure, volume and temperatue. They expand to the same final volume, one adiabatically and the other isothermally
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Work done is equal to area under the P-V graph, thus work done by gas is greater for isothermal process.
For isothermal process: $T_{2}=T_{o}$
For adibatic process: $T_{o}\left(V_{o}\right)^{\gamma-1}=T(V)^{\gamma-1}$
As $V>V_{o} \Longrightarrow T Thus final temp. is greater for isothermal process. For isothermal process: $P_{o} V_{o}=P_{i} V \quad \Longrightarrow P_{i}=P_{o} \frac{V_{o}}{V}$ For adibatic process: $P_{o}\left(V_{o}\right)^{\gamma}=P_{a}(V)^{\gamma}$ $\Longrightarrow P_{a}=P_{o}\left(\frac{V_{o}}{V}\right)^{\gamma}$ As $\gamma>1 \quad$ (always) $\Longrightarrow P_{i}>P_{a}$
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