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Standard XII

Physics

1st Law of Thermodynamics

N moles of ga...

Question

$N m o l e s$ of gas an ideal mono atomic gas is confined in a cylinder A of volume $V_{0}$ , pressure $P_{0}$ and temperature $T_{0}$ , this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is 7 $V_{0}$ and B is evacuated and then stop-cork is opened so that gas expands and occupies the volume $8 V_{0}$ .
[System is thermally isolated from the surroundings].

Now with the stop-cork open. The piston is slowly moved to compress the gas back to cylinder A. For this work done on the gas :

\frac{9}{2} n R T_{0}

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n R T_{0} ln 2

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\frac{7}{2} n R T_{0}

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- 3 n R T_{0} ln 2

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Solution

The correct option is A $\frac{9}{2} n R T_{0}$
Taking adiabatic compression, final temperature $= 4 T_{0} u s i n g T V^{- 1} = c o n s t a n t$
So, work done by the gas W $= \frac{- n R Δ T}{γ - 1} = - \frac{9}{2} n R T_{0}$

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The correct option is A 92nRT0Taking adiabatic compression, final temperature=4T0 using TV−1=constantSo, work done by the gas W=−nRΔTγ−1=−92nRT0

The correct option is A $\frac{9}{2} n R T_{0}$
Taking adiabatic compression, final temperature $= 4 T_{0} u s i n g T V^{- 1} = c o n s t a n t$
So, work done by the gas W $= \frac{- n R Δ T}{γ - 1} = - \frac{9}{2} n R T_{0}$