The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} C$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is

$A$ jar $P$ is filled with a gas having pressure,volume,and temperature $P, V, T$ respectively. Another gas jar $Q$ is filled with a gas having pressure $2P$,volume $\frac{V}{4}$,and temperature $2T$. The ratio of the number of molecules in jar $P$ to those in jar $Q$ is:

An insulated container is divided into two parts by a partition. The same gas is filled in both parts. In the right part,the volume,temperature,and pressure are $2V$,$T$,and $2P$ respectively. In the left part,the same parameters are $V$,$T$,and $P$. What is the ratio of the number of molecules in the right part to the left part?

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/2$ is given by the straight line

At a temperature $T \ K$,the pressure of $4.0 \ g$ argon in a bulb is $p$. The bulb is put in a bath having a temperature higher by $50 \ K$ than the first one. $0.8 \ g$ of argon gas had to be removed to maintain the original pressure. The temperature $T$ is equal to ..... $K$.

The volume occupied by the molecules contained in $4.5 \, kg$ of water at $STP$,if the intermolecular forces vanish away,is ........ $m^{3}$.