Question

Suppose ideal gas equation follows $V{P}^3=$ 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: $V{P}^3=$ 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 $T_2=9T_1=9T$