Question

One mole of oxygen is allowed to expand isothermally and reversibly from 5 metre cube to 10 metre cube at 300 kelvin calculate the work done in expansion of the gas

Answer 1

Given

Number of moles = 1 mole of O₂

Process is isothermal and reversible.

Initial volume = 5m³

Final volume = 10m³

Temperature = 300 K

So now, Work done during this process is

$W \: = - 2.303nRT log( \frac{V _{2}} {V _{1}} )$

Work done is,

$W \: = - 2.303nRT log( \frac{V _{2}} {V _{1}} ) \\ \\ W = - 2.303 \times (1)(2)(300) log( \frac{10}{5} ) \\ \\ W = - 2.303 \times 600 \times log2 \\ \\ W = - 1381.8 \times 0.3010 \\ \\ W = - 415.9218 \: cal$

Therefore, The work done during this isothermal expansion is nearest 416 Calories.