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Question

During an experiment, an ideal gas is found to obey a law VP2= constant. The gas is initially at temperature T and volume V. When it expands to volume 2V, the resulting temperature will be

A
5 T
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B
3 T
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C
2 T
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D
6 T
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Solution

The correct option is C 2 T
Given that,
Initial temperature, Ti=T
Initial volume, Vi=V
Final volume, Vf=2V
Final temperature, Tf=?

VP2= constant ..............(1)
From the ideal gas equation,
PV=nRT
P=nRTV ..............(2)
From equation (1) and (2)
V(nRTV)2= constant
n2R2T2VV2= constant
T2V= constant
[ n and R are constant ]
So,
T2fVf=T2iVi
T2f2V=T2V
Tf=2 T

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