Question

Find the amount of work done to increase the temperature of one mole of ideal gas by ${30}^{o}C$. If it is expanding under the condition $V\propto T^{2/3}(R=8.31J/mol-K)$

• A. 16.62 J
• B. 166.2 J
• C. 1662 J
• D. 1.662 J

Answer 1

The correct option is B 166.2 J

Under the condition V directly proportional to $T^{2/3}$

we get, $T{V}^{3/2}=k^{3/2}$ (constant)

Relating from the eqn. $T{V}^{Y-1}=K_0$ (CONSTANT)

$Y-1=\frac{3}{2}$

$Y=1+\frac{3}{2}$

$Y=\frac{5}{2}$ .

Now, $W=\frac{\left(nRT\right)}{(1-Y)}$

putting above value,

$W=\frac{(1\ast R\ast {30}^O)}{(1-5/2)}$=$\frac{\left(30R\right)}{\left(3/2\right)}=166.2J$