Q.
The density $(\rho)$ versus pressure $(P)$ of a given mass of an ideal gas is shown at two temperatures $T_{1}$ and $T_{2}$
Then relation between $T_{1}$ and $T_{2}$ may be
A) $T_{1} > T_{2}$
B) $T_{2} > T_{1}$
C) $T_{1} = T_{2}$
D) All the three are possible
Explanation
(b) According to ideal gas equation $PV = nRT$
$PV = \frac{m}{M}RT,\ P = \frac{\rho}{M}RT$ or $\frac{\rho}{P} = \frac{M}{RT}$or $\frac{\rho}{P} \propto \frac{1}{T}$
Here, $\frac{\rho}{P}$ represent the slope of graph
Hence $T_{2} > T_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.