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Question

# Suppose an ideal gas undergoes a process given by VP3=constant. Initial temperature and volume of the gas are T and V respectively. If the gas expands to 27V, then its temperature will become

A
T
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B
9T
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C
27T
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D
T9
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Solution

## The correct option is B 9T Given,VP3=constant=k3 (say) ⇒P=kV1/3 ......(1) Also for an ideal gas, PV=nRT Using (1) in the above ideal gas equation, we get kV1/3.V=nRT⇒V2/3=nRTk ∴ we can say that, V2/3∝T Hence, (V1V2)2/3=T1T2 .....(2) Given, Initial temperature (T1)=T Initial volume (V1)=V Final volume (V2)=27V Final temperature (T2)=? Equation (2) becomes (V27V)2/3=TT2⇒T2=9T Thus, option (b) is the correct answer.

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