Question

The work done in adiabatic compression of $2$ mole of an ideal monoatomic gas by constant external pressure of $2$ atm starting from initial pressure of $1$ atm and initial temperature of $300K$ ($R=2$ cal/mol-degree celsius) is :

• A. $360cal$
• B. $720cal$
• C. $800cal$
• D. $1000cal$

Answer 1

Answer: (B)

$720cal$

$q=0$, $\Delta U=W$
$n{C}_V(T_2-T_1)=-P_{ext}(V_2-V_1)$

$n\frac{3}{2}R(T_2-300)=-2(\frac{nR{T}_2}{2}-\frac{nR\times 300}{1})$

$\Rightarrow \frac{3}{2}(T_2-300)=(600-T_2)\Rightarrow T_2=420K$

$W=n{C}_V(T_2-T_1)=2\times \frac{3}{2}\times 2(420-300)=720cal$