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One mole of an ideal gas at temperature T1 expands slowly according to the law p/v =constant.The final temperature is T2 the workdone by the gas is

One mole of an ideal gas at temperature T1 expands slowly according to the law p/v =constant.The final temperature is T2 the workdone by the gas is

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Grade:12

2 Answers

Khimraj
3007 Points
3 years ago
Let P/V = a(constant)
then work done = \int Pdv = \intaVdv\intaVdv\int_{v1}^{v2}avdv = (a/2)(v22 – v12)
Now PV = nRT
n = 1,
P = aV
So V2 = RT/a
So v22 = RT2/a
and V12 = RT1/a
So work done
W = R(T2 – T1)/2
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

One mole of an ideal gas at temperature t1 expands according to the law p/v =constant.The final temperature is T2.
Suppose P/V = a(constant)
then work done = \int Pdv = \int aVdv\int aVdv\int_{v1}^{v2}avdv = (a/2)(v2square – v1square)
Now PV = nRT , n = 1,
PV = RT
P = aV
V square = RT/a
So v2 square = RT2/a
and V1 square = RT1/a
work done: W = R(T2 – T1)/2

Thanks and Regards

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