Q. 18

For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression w = – nRT ln

A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and 600 K respectively. Choose the correct option.

A. Work done at 600 K is 20 times the work done at 300 K.

B. Work done at 300 K is twice the work done at 600 K.

C. Work done at 600 K is twice the work done at 300 K.

D. ΔU = 0 in both cases.

Answer :

Reason:

As we all know the below relation Vf


w = -nRT ln


Here R, T, and ln are the same in both cases, sowork done will only depend on the temperature.


= = = 2


Here w2 indicates work done at 600K


w1indicates work done at 300k


so, from the above expression, it is clear that work done at 600K is twice the work done at 300k.


(iv)Internal energy depends on the temperature and it is given that the above process is isothermal, which indicates ΔU=0, in both the cases.

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