Question

In any isothermal reversible expansion if the volume of 96g of oxygen at 27C is increased from 70 lit to 140lit then the work done by the gas will be​

Answer 1

Solution:

As per the given data,

• Mass of oxygen(m) = 96 g
• Molar mass of oxygen (M)= 32 g (diatomic)
• Temperature(T) = 27°C = 273 +27 = 300 K
• Initial volume(V₁) = 70 L
• Final volume (V₂) = 140 L

Work done by the gas during the isothermal reversible process is given by,

$\implies\sf{W= 2.303 nRT log\bigg(\dfrac{V_2}{V_1}\bigg)}$

$\implies\boxed{\sf{W= 2.303 \dfrac{m}{M}RT log_{10}\bigg(\dfrac{V_2}{V_1}\bigg)}}$

Now let's substitute the values,

$\implies\sf{W= 2.303 \bigg(\dfrac{96}{32}\bigg)\times 0.082\times273 \:log_{10}\bigg(\dfrac{140}{70}\bigg)}$

$\implies\sf{W= 2.303 \times 3 \times 0.082\times273 \:log_{10}2 }$

$\implies\sf{W= 2.303 \times 3 \times 0.082\times273 \times 0.3010 }$

$\implies\boxed{\sf{W= 46.26 J }}$

The work done by the gas will be 46.26 J.