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Question

# The state of an ideal gas is changed through an isothermal process at temperature To as shown in figure. The work done by gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is Po2, then pressure of the gas in state C is

A
Po3
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B
Po4
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C
Po6
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D
Po8
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Solution

## The correct option is B Po8Given : PA=Po PB=Po2Let the pressure at C be PC.Workdone in isothermal process from A to B, WAB=nRTln(PAPB) ∴ WAB=nRTln(PoPo/2)=nRT ln2Workdone in isothermal process from B to C, WBC=nRTln(PBPC) ∴ WBC=nRTln(Po2PC) According to question, WBC=2WAB∴ nRTln(Po2PC)= 2nRT ln2 ln(Po2PC)= ln4 ⟹Po2PC=4⟹ PC=Po8

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