$A$ vessel contains $16 \,g$ of hydrogen and $128 \,g$ of oxygen at standard temperature and pressure $(STP)$. The volume of the vessel in $cm^{3}$ is:

The pressure versus temperature graph of an ideal gas with an equal number of moles at different volumes is plotted as shown in the figure. Choose the correct alternative.

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P = P_0 \left[ 1 - \frac{1}{2} \left( \frac{V_0}{V} \right)^2 \right]$. Here $P_0$ and $V_0$ are constants. Calculate the change in the temperature of the gas if its volume changes from $V_0$ to $2V_0$.

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

Air is filled at $60^{\circ} C$ in a vessel of open mouth. The vessel is heated to a temperature $t^{\circ} C$ so that $\frac{1}{4}$th of the air escapes from the vessel. Assuming air as an ideal gas and the volume of the vessel remains constant, the value of '$t$' is: (in $^{\circ} C$)

The gas law $\frac{PV}{T} = \text{constant}$ is true for