Q. No.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 \(10^{\circ}\text{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x.\) At \(110^{\circ}\text{C}\) 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 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. |
The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\)
3. \(r\)
4. \(\sqrt{r}\)
| 1. | \(\left(1+\frac{1}{n}\right )\) | 2. | \(\left(1+\frac{n}{3}\right)\) |
| 3. | \(\left(1+\frac{2}{n}\right)\) | 4. | \(\left(1+\frac{n}{2}\right)\) |
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. | \(20~\text{kJ}\) | 2. | \(-20~\text{kJ}\) |
| 3. | \(20~\text{J}\) | 4. | \(-12~\text{kJ}\) |
Two vessels separately contain two ideal gases \(A\) and \(B\) at the same temperature, the pressure of \(A\) being twice that of \(B.\) Under such conditions, the density of \(A\) is found to be \(1.5\) times the density of \(B.\) The ratio of molecular weight of \(A\) and \(B\) is:
| 1. | \(\dfrac{2}{3}\) | 2. | \(\dfrac{3}{4}\) |
| 3. | \(2\) | 4. | \(\dfrac{1}{2}\) |
1. \(\frac{400}{\sqrt{3}}\)
2. \(\frac{100\sqrt{2}}{3}\)
3. \(\frac{100}{3}\)
4. \(100\sqrt{2}\)
A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:
| 1. | \(15RT\) | 2. | \(9RT\) |
| 3. | \(11RT\) | 4. | \(4RT\) |
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. \(mkT\)
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