The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. The gas in another jar $B$ is at pressure $2P$,volume $V/4$,and temperature $T/4$. What is the ratio of the number of molecules in jar $A$ to jar $B$?

The correct graph between pressure $(P)$ and density $(\rho)$ of a gas at constant temperature is

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

By using the ideal gas equation $PV = \mu RT$,write the value,unit,and dimension of $R$.

The equation of an ideal gas in terms of pressure $(P)$,absolute temperature $(T)$,and density $(d)$ is:

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the piston,it moves down. If the air in the enclosure is cooled from temperature $T$ to $T-\Delta T$,the piston moves back to its original position. Then $\Delta T / T$ is close to (Assuming air to be an ideal gas,$g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$)