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If a certain mass of gas is made to undergo separately adiabatic and isothermal expansion to the same pressure, starting from the same initial condition of temperature and pressure, then, as compared to that of isothermal expansion, in the case of adiabatic expansion, the final

A
volume and temperature will be higher
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B
volume and temperature will be lower
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C
temperature will be lower but the final volume will be higher
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D
volume will be lower but the final volume will be higher
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Solution

The correct option is D temperature will be lower but the final volume will be higher
We know for an adiabatic process,
P1Vγ1 = P2Vγ2
For an isothermal process,
P1V1 = P2V2
Given, Initial temperatures, pressures,and volumes and final pressures are same for both the processes.
For an adiabatic process,
P1Vγ1 = P2Vγ2...........(1)
where V2 is the final volume for an adiabatic process

For an isothermal process,
P1V1 = P2V3.............(2)
where V3 is the final volume for an isothermal process.
The ratio of (1) and (2)

1= Vγ2V3
since γ is greater than 1, V3 must be greater than V2
similarly,
For an adiabatic process,
P1γ1Tγ1=P1γ2Tγ2
Temperature decreases with pressure.
For an isothermal process,
Initial and final temperature will be same.
T2<T1

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