The figure below shows the graph of pressure and volume of a gas at two temperatures and . Which one, of the following, inferences is correct?
1. | \(\mathrm{T}_1>\mathrm{T}_2\) |
2. | \(\mathrm{T}_1=\mathrm{T}_2\) |
3. | \(\mathrm{T}_1<\mathrm{T}_2\) |
4. | No inference can be drawn |
An ideal gas is initially at temperature T and volume V. Its volume increases by due to an increase in temperature , pressure remaining constant. The quantity varies with temperature as:
1. | 2. | ||
3. | 4. |
Which one, of the following, graphs represents the behaviour of an ideal gas at constant temperature?
1. | 2. | ||
3. | 4. |
An experiment is carried out on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of with P is shown in the diagram. The correct variation will correspond to: (Assuming that the gas in consideration is nitrogen)
1. | Curve A | 2. | Curve B |
3. | Curve C | 4. | Curve D |
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at \(300\) K. The ratio of the average rotational kinetic energy per molecule to that per molecule is:
1. | 1 : 1 |
2. | 1 : 2 |
3. | 2 : 1 |
4. | depends on the moments of inertia of the two molecules |
The root mean square speed of the molecules of a diatomic gas is \(v\). When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is:
1. | \(\sqrt{2}v\) | 2. | \(v\) |
3. | \(2v\) | 4. | \(4v\) |
Two containers of equal volumes contain the same gas at pressures \(P_1\) and \(P_2\) and absolute temperatures \(T_1\) and \(T_2\), respectively. On joining the vessels, the gas reaches a common pressure \(P\) and common temperature \(T\). The ratio \(\frac{P}{T}\) is equal to:
1. | \(\frac{P_1}{T_1}+\frac{P_2}{T_2}\) | 2. | \(\frac{P_1T_1+P_2T_2}{(T_1+T_2)^2}\) |
3. | \(\frac{P_1T_2+P_2T_1}{(T_1+T_2)^2}\) | 4. | \(\frac{P_1}{2T_1}+\frac{P_2}{2T_2}\) |
The average translational kinetic energy of \(O_2\) (molar mass \(32\)) molecules at a particular temperature is \(0.048~\text{eV}\). The translational kinetic energy of \(N_2\) (molar mass \(28\)) molecules in \(\text{eV}\) at the same temperature is:
1. \(0.0015\)
2. \(0.003\)
3. \(0.048\)
4. \(0.768\)
The translatory kinetic energy of a gas per \(\text{g}\) is:
1. | \({3 \over 2}{RT \over N}\) | 2. | \({3 \over 2}{RT \over M}\) |
3. | \({3 \over 2}RT \) | 4. | \({3 \over 2}NKT\) |
For hydrogen gas \(C_P-C_V=a\) and for oxygen gas \(C_P-C_V=b\) where molar specific heats are given. So the relation between \(a\) and \(b\) is given by:
(where \(C_P\) and \(C_V\) in \(\text{J mol}^{-1}\text{K}^{-1}\))
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)