Question

2 moles of a monoatomic gas are expanded to double its initial volume, through a process P/V = constant. If its initial temperature is 300K, then which of the following is not true.

• A. $\Delta T=900K$
• B. $\Delta Q=3200K$
• C. $\Delta Q=3600K$
• D. $\Delta W=900K$

Answer 1

The correct option is C $\Delta Q=3600K$

Given :2 moles of a monoatomic gas are expanded to double its initial volume, through a process P/V = constant. If its initial temperature is 300K, then which of the following is not true.

Solution :

$\frac{P}{V}=constant$=C

PV=nRT

$C{V}^2=nRT$

$\frac{V_1^2}{V_2^2}=\frac{T_1}{T_2}$

$V_1=V$ and $V_2=2V$, $T_1=300k$

On solving we get $T_2=1200K$ then $\Delta T=900K$

Work done =$\int P.dv$

Work done =${\int }_v^{2v}CV.dv$ = $\frac{3}{2}C{V}^2$ =$\frac{3}{2}nRT$

Work done=$\frac{3}{2}\times 2\times R\times 300$ = 900R

$\Delta Q=\Delta U+\Delta W$

$\Delta U=n{C}_v\Delta T$

$\Delta U=2\times \frac{3R}{2}\times 900$ = 2700R

$\Delta Q=900R+2700R$ = 3600R