Q. Suppose ideal gas equation follows $VP^{3} =$ constant. Initial temperature and volume of the gas are $T$ and $V$ respectively. If gas expands to $27\ V$ then its temperature will become
A) $T$
B) $9T$
C) $27\ T$
D) $T/9$
Explanation
(b) $VP^{3} =$ constant $= k \Rightarrow P = \frac{k}{V^{1/3}}$
Also $PV = \mu RT \Rightarrow \frac{k}{V^{1/3}}.V = \mu RT \Rightarrow V^{2/3} = \frac{\mu RT}{k}$
Hence $\left( \frac{V_{1}}{V_{2}} \right)^{2/3} = \frac{T_{1}}{T_{2}} \Rightarrow \left( \frac{V}{27V} \right)^{2/3} = \frac{T}{T_{2}} \Rightarrow T_{2} = 9T$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.