1 mole of an ideal gas expands isothermally reversible from 2 litre to 4 litre and 3 moles of the same gas expands from 2 litre to x litre and doing same work, what is 'x'-

Options

A. `(8)^(1//3)`
B. `(4)^(2//3)`
C. 2
D. 4

Answer

B

Explanation

`w=-nRT"ln"(V_(2))/(V_(1)) or, RT"ln"(4)/(2)=3RT"ln"(x)/(2)`
or, `ln2=ln((x)/(2))^(3) or, (x^(3)=16)or,x=(16)^((1)/(3))=4^((2)/(3))`.