Question

# One mole of a monoatomic ideal gas occupies two chambers of a cylinder partitioned by means of a movable piston. The walls of the cylinder as well as the piston are thermal insulators. Initially, equal amounts of gas fill both the chambers at (P0,V0,T0). A coil is burnt in the left chamber which causes the gas to absorb heat and expand, pushing the piston to the right. The gas in the right chamber is compressed until the pressure is 32P0 Choose the correct options.

A
The final volume of the left chamber is 15V08.
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B
The final volume of the left chamber is 9V08.
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C
The work done on the gas in the right chamber is 12P0V0.
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D
The work done on the gas in the right chamber is 92P0V0
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Solution

## The correct options are A The final volume of the left chamber is 15V08. D The work done on the gas in the right chamber is 92P0V0Since the compression on the right is adiabatic P0Vγ0=PRVγR P0V530=32P0V53R (∵ Monoatomic gas and given PR=32 P0) ⇒VR=18V0 and VL=V0+78V0=158V0 Work done on the gas =PRVR−P0V0γ−1 PRVR=32P0×V08=4P0V0 ∴ Work done =P0V0−4P0V053−1 =92P0V0 (∵ monoatomic gas)

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