Q. No.The molecules of a given mass of gas have RMS velocity of \(200~\text{ms}^{-1}\) at \(27^\circ \text{C}\) and \(1.0\times 10^{5}~\text{Nm}^{-2}\) pressure. When the temperature and the pressure of the gas are respectively, \(127^\circ \text{C}\) and \(0.05\times10^{5}~\text{Nm}^{-2},\) the RMS velocity of its molecules in \((\text{ms}^{-1})\) is:
1.
\(\dfrac{400}{\sqrt{3}}\)
2.
\(\dfrac{100\sqrt{2}}{3}\)
3.
\(\dfrac{100}{3}\)
4.
\(100\sqrt{2}\)
| 1. | \(\dfrac{400}{\sqrt{3}}\) | 2. | \(\dfrac{100\sqrt{2}}{3}\) |
| 3. | \(\dfrac{100}{3}\) | 4. | \(100\sqrt{2}\) |
\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\))
| 1. | \(8.0~\text{JK}^{-1}\text{mol}^{-1}\) | 2. | \(7.5~\text{JK}^{-1}\text{mol}^{-1}\) |
| 3. | \(7.0~\text{JK}^{-1}\text{mol}^{-1}\) | 4. | \(8.5~\text{JK}^{-1}\text{mol}^{-1}\) |
| 1. | \(\dfrac{2}{3}\) | 2. | \(\dfrac{3}{4}\) |
| 3. | \(2\) | 4. | \(\dfrac{1}{2}\) |
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. | \(20~\text{kJ}\) | 2. | \(-20~\text{kJ}\) |
| 3. | \(20~\text{J}\) | 4. | \(-12~\text{kJ}\) |
| 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 \(10^{\circ}\text{C}\) 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. |
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. | \(4RT\) |
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