Question

Calculate the work done when $1.6\times {10}^{-2}$ kg of oxygen at $300$K are expanded isothermally and reversibly till the volume is increased four times.

Answer 1

Solution:-

As we know that, work done in an isothermal reversible expansion is given as-

$W=-2.303\times nRT\times \log \frac{V_f}{V_i}$

Let $V$ be the initial volume.

$\therefore V_f=4V$

Given:-

Wt. of oxygen $=1.6\times {10}^{-2}kg=16g$

Mol. wt. of oxygen $=32g$

Therefore, no. of moles of oxygen in $16g=\frac{16}{32}=0.5\text{mole}$

$T=300K$

$W=-2.303\times 0.5\times 8.314\times 300\times \log \frac{4V}{V}$

$\Rightarrow W=-2872.07\times \log 4$

$\Rightarrow W=-1729.16J$

Hence the work done is $-1729.16J$.