For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression W=-nRTlnVfVi. A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversible to ten times of its original volume, in to separate experiments. The expansion is carried out at 300 K and at 600 K respectively. Choose the correct option.

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

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

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

4.  U=0 in both cases

(c, d)
Given that, the work of reversible expansion under isothermal condition can be calculated by using the expression
W=-nRTlnVfVi
Vf=10Vi
T2=600K
T1=300K
Putting these values in above expression
W600K=1×R×600Kln101
W300K=1×R×300Kln101
Ration=W600KW300K=1×R×600Kln1011×R×300Kln101=600300=2
For isothermal expansion of ideal gases, U=0. Since, temperature is constant this means there is no change is internal energy.