$A$ cylindrical tube of uniform cross-sectional area $A$ is fitted with two airtight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is $P_0$ and the temperature is $T_0$; the atmospheric pressure is also $P_0$. Now, the temperature of the gas is increased to $2T_0$. The tension in the wire will be:

$A$ diatomic gas of molecular weight $30 \, g/mol$ is filled in a container at $27 \, ^\circ C$. It is moving at a velocity of $100 \, m/s$. If it is suddenly stopped,the rise in temperature of the gas is:

$A$ thermally isolated cylindrical closed vessel of height $8 \ m$ is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass $8.3 \ kg$. Thus,the partition is held initially at a distance of $4 \ m$ from the top. Each of the two parts of the vessel contains $0.1 \ mol$ of an ideal gas at temperature $300 \ K$. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached,the distance of the partition from the top (in $m$) will be. . . . . . (take the acceleration due to gravity $g = 10 \ m/s^2$ and the universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$).

Which one of the following schematic graphs best represents the variation of $p V$ (in Joules) versus $T$ (in Kelvin) of one mole of an ideal gas? (The dotted line represents $p V=T$)

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then

From a certain apparatus,the diffusion rate of hydrogen has an average value of $28.7 \; cm^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2 \; cm^3 s^{-1}$. Identify the gas.