Question

Suppose an ideal gas follows equation V$P^3$ = constant. Initial temperature and volume of the gas are T and V respectively. If gas expands to 27V then its temperature will be come

• A. T
• B. 9T
• C. 27T
• D. T/9

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