Test Index

Heat and Thermodynamics

Section: Physics

Question : 6 of 78

Marks: +1, -0

Solution:

The work done when a gas changes its volume at constant temperature (isothermal process) is given by:

W = n R T \ln \left( \frac{V_2}{V_1} \right)

First Case: From

V

2 V

We have

n=2, V_1=V

, and

V_2=2 V

So, the work done is:

W = 2 R T \ln \left( \frac{2V}{V} \right) = 2 R T \ln(2)

Second Case: From

2 V

4 V

Now,

n=2, V_1=2 V

, and

V_2=4 V

So, the work done here is:

W' = 2 R T \ln \left( \frac{4V}{2V} \right)

= 2 R T \ln(2) = W

The work done in increasing the volume from

2 V

4 V

is the same as the work done from

V

2 V

, both are

W

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