An insulated container contains $4$ moles of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to the gas,causing $2$ moles of the gas to dissociate into atoms. If the temperature of the gas remains constant,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.

Which of the following graphs represents the variation of $\beta = -(dV/dP)$ with pressure $P$ for an ideal gas kept at a constant temperature?

If a gas is heated at constant pressure,its isothermal compressibility

Following statements are given:
$(1)$ The average kinetic energy of a gas molecule decreases when the temperature is reduced.
$(2)$ The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
$(3)$ The average kinetic energy of a gas molecule decreases with increase in volume.
$(4)$ Pressure of a gas increases with increase in temperature at constant volume.
$(5)$ The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

$A$ vessel contains $14 \, g$ ($7$ moles) of hydrogen and $96 \, g$ ($3$ moles) of oxygen at $STP$. $A$ chemical reaction is induced by passing an electric spark in the vessel until one of the gases is consumed. The temperature is brought back to its starting value of $273 \, K$. The pressure in the vessel is ...... $atm$.