A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?
1. \(\frac{P}{kT}\)
2. \(\frac{Pm}{kT}\)
3. \(\frac{P}{kTV}\)
4. \(mkT\)
A gas mixture consists of \(2\) moles of \(O_2\) and \(4\) moles of \(Ar\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:
1. | \(15RT\) | 2. | \(9RT\) |
3. | \(11RT\) | 4. | \(4RT\) |
Two vessels separately contain two ideal gases \(\mathrm{A}\) and \(\mathrm{B}\) at the same temperature, the pressure of \(\mathrm{A}\) being twice that of \(\mathrm{B}\). Under such conditions, the density of \(\mathrm{A}\) is found to be \(1.5\) times the density of \(\mathrm{B}\). The ratio of molecular weight of \(\mathrm{A}\) and \(\mathrm{B}\) is:
1. | \(\frac{2}{3}\) | 2. | \(\frac{3}{4}\) |
3. | \(2\) | 4. | \(\frac{1}{2}\) |
One mole of an ideal diatomic gas undergoes a transition from \(A\) to \(B\) along a path \(AB\) as shown in the figure.
The change in internal energy of the gas during the transition is:
1. | \(20\) kJ | 2. | \(-20\) kJ |
3. | \(20\) J | 4. | \(-12\) kJ |
The ratio of the specific heats \(\frac{{C}_{{P}}}{{C}_{{V}}}=\gamma\) in terms of degrees of freedom(\(n\)) is given by:
1. | \(\left(1+\frac{1}{n}\right )\) | 2. | \(\left(1+\frac{n}{3}\right)\) |
3. | \(\left(1+\frac{2}{n}\right)\) | 4. | \(\left(1+\frac{n}{2}\right)\) |
The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\)
3. \(r\)
4. \(\sqrt{r}\)
In the given \({(V\text{-}T)}\) diagram, what is the relation between pressure \({P_1}\) and \({P_2}\)?
1. | \(P_2>P_1\) | 2. | \(P_2<P_1\) |
3. | cannot be predicted | 4. | \(P_2=P_1\) |
At \(10^{\circ}\mathrm{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x\). At \(110^{\circ}\mathrm{C}\) this ratio is:
1. | \(x\) | 2. | \(\dfrac{383}{283}x\) |
3. | \(\dfrac{10}{110}x\) | 4. | \(\dfrac{283}{383}x\) |
An increase in the temperature of a gas-filled in a container would lead to:
1. decrease in intermolecular distance.
2. increase in its mass.
3. increase in its kinetic energy.
4. decrease in its pressure.