Q. At $0℃$ the density of a fixed mass of a gas divided by pressure is $x.$ At $100℃,$ the ratio will be
A) $x$
B) $\frac{273}{373}x$
C) $\frac{373}{273}x$
D) $\frac{100}{273}x$
Explanation
(b) $PV = \mu\ RT = \frac{m}{M}RT \Rightarrow \frac{m}{VP} \Rightarrow \frac{density}{P} = \frac{M}{RT}$
$\left( \frac{density}{P} \right)_{At\ 0℃} = \frac{M}{R(273)} = x$ …(i)
$\left( \frac{density}{P} \right)_{At\ 100℃} = \frac{M}{R(373)}$ …(ii)
$\Rightarrow \left( \frac{density}{P} \right)_{At\ 100℃} = \frac{273x}{373}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.