An increase in the temperature of a gas-filled in a container would lead to:
1. | decrease in the intermolecular distance. |
2. | increase in its mass. |
3. | increase in its kinetic energy. |
4. | decrease in its pressure. |
Match Column I and Column II and choose the correct match from the given choices.
Column I | Column II | ||
(A) | root mean square speed of gas molecules | (P) | \(\dfrac13nm\bar v^2\) |
(B) | the pressure exerted by an ideal gas | (Q) | \( \sqrt{\dfrac{3 R T}{M}} \) |
(C) | the average kinetic energy of a molecule | (R) | \( \dfrac{5}{2} R T \) |
(D) | the total internal energy of \(1\) mole of a diatomic gas | (S) | \(\dfrac32k_BT\) |
(A) | (B) | (C) | (D) | |
1. | (Q) | (P) | (S) | (R) |
2. | (R) | (Q) | (P) | (S) |
3. | (R) | (P) | (S) | (Q) |
4. | (Q) | (R) | (S) | (P) |
1. | \(379\) J | 2. | \(357\) J |
3. | \(457\) J | 4. | \(374\) J |
Uranium has two isotopes of masses \(235 \) and \(238\) units. If both are present in Uranium hexafluoride gas, which would have the larger average speed?
1. \(^{235} \mathrm{U} \mathrm{F}_{6}\)
2. \({}^{238} \mathrm{U} \mathrm{F}_{6}\)
3. Both will have the same average speed.
4. Data insufficient
The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the gas constant)
1. PV = 5 RT
2. PV = (5/2) RT
3. PV = (5/16) RT
4. PV = (5/32) RT
To find out the degree of freedom, the correct expression is:
1.
2.
3.
4.
If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)
The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1. | \(l\propto \dfrac{1}{d^2}\) | 2. | \(l\propto d\) |
3. | \(l\propto d^2 \) | 4. | \(l\propto \dfrac{1}{d}\) |
Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory, \(PV = \dfrac{2}{3}E\) \(E\) is:
1. | the total energy per unit volume. |
2. | only the translational part of energy because rotational energy is very small compared to translational energy. |
3. | only the translational part of the energy because during collisions with the wall, pressure relates to change in linear momentum. |
4. | the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero. |
\(1\) mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at \(300\) K (figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time:
1. | the pressure on EFGH would be zero. |
2. | the pressure on all the faces will be equal. |
3. | the pressure on EFGH would be double the pressure on ABCD. |
4. | the pressure on EFGH would be half that on ABCD. |