Question

Suppose ideal gas equation follows $V{P}^3=constant$. Initial temperature and volume of the gas are T and V respectively. If gas expand to 27V then its temperature will become

• A. $T$
• B. $9T$
• C. $27T$
• D. $\left(\frac{T}{9}\right)$

Answer 1

The correct option is B

$9T$

$V{P}^3=constant=k\Rightarrow P=\frac{k}{V^{\frac{1}{3}}}$
Also $PV=\mu RT\Rightarrow \frac{k}{V^{\frac{1}{3}}}V=\mu RT$ $\Rightarrow V^{\frac{2}{3}}=\frac{\mu RT}{k}$
Hence ${\left(\frac{V_1}{V_2}\right)}^{\frac{2}{3}}=\frac{T_1}{T_2}$ $\Rightarrow {\left(\frac{V}{27V}\right)}^{\frac{2}{3}}=\frac{T}{T_2}\Rightarrow T_2=9T$