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?

An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{-7} \text{ mm}$ of mercury at $27^{\circ}C$. Its volume is $100 \text{ cm}^3$. The number of molecules that remain in the tube is

When the pressure of the gas contained in a closed vessel is increased by $2.5 \%$,the temperature of the gas increases by $4 \ K$. The initial temperature of the gas is (in $K$)

Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature $T$. Bulb $2$ is heated to maintain a temperature $2 T$,while bulb $1$ remains at temperature $T$. Assume throughout that the heat conduction by the capillary is negligible. Then,the ratio of final mass of the gas in bulb $2$ to the initial mass of the gas in the same bulb is close to

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then:

Pressure of a gas of constant volume at $20^{\circ} C$ is $90 \ cm$ of $Hg$. At what temperature the pressure would change to $75 \ cm$ of $Hg$ (in $^{\circ} C$)?