Question

Suppose ideal gas equation follows $VP^3 =$ constant. Initial temperature and volume of gas are T and V respectively. If gas expands to 27V, then its temperature will become

• A. $T$
• B. $9T$
• C. $27T$
• D. $\frac{T}{9}$

Answer 1

Answer: (B)

Given: $VP^3 =$ constant $= k$ or $P = \frac{k}{V^{1/3}}$
According to ideal gas equation,
$PV = nRT$
$\therefore \frac{k}{V^{1/3}} V = nRT$ or $V^{2/3} = \frac{nTR}{k}$
Hence, $\left(\frac{V_{1}}{V_{2}}\right)^{2/3} = \frac{T_{1}}{T_{2}}$
$\left[\frac{V}{27V}\right]^{2/3} = \frac{T_{1}}{T_{2}}$ or $T_{2} = 9\,T_{1} = 9T$