An ideal gas initially at pressure $1 \, bar$ is being compressed from $30 \, m^{3}$ to $10 \, m^{3}$ volume and its temperature decreases from $320 \, K$ to $280 \, K$. Find the final pressure of the gas (in $bar$).

Under constant temperature,the graph between $P$ and $1/V$ is:

$A$ vessel containing $5 \, L$ of a gas at $0.8 \, Pa$ pressure is connected to an evacuated vessel of volume $3 \, L$. The resultant pressure inside will be ...... $Pa$ (assuming the whole system to be isolated).

The $P-T$ graph shows a gas being heated. During this process from point $1$ to $2$,the volume of the gas:

In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

An ideal gas has pressure $P$,volume $V$ and absolute temperature $T$. If $m$ is the mass of each molecule and $K$ is the Boltzmann constant,then the density of the gas is: