Assertion (A): | If a gas container in motion is suddenly stopped, the temperature of the gas rises. |
Reason (R): | The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Assertion (A): | The ratio \(C_p\over C_v\) is more for helium gas than for hydrogen gas. |
Reason (R): | Atomic mass of helium is more than that of hydrogen. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
(A) | \(n\) degrees of freedom has \(n^2\) different ways of storing energy. | A molecule with
(B) | \(\dfrac{1}{2} R T\) per mole. | Each degree of freedom is associated with an average energy of
(C) | A monoatomic gas molecule has \(1\) rotational degree of freedom whereas a diatomic molecule has \(2\) rotational degrees of freedom. |
(D) | \(CH_4\) has a total of \(6\) degrees of freedom. |
1. | (B) and (C) only |
2. | (B) and (D) only |
3. | (A) and (B) only |
4. | (C) and (D) only |
A. | \((\overline{v^2})\). | They have an equal mean square velocity
B. | \((\overline{v^2})\) than an oxygen molecule. | A nitrogen molecule has a greater mean square velocity
C. | A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule. |
D. | An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule. |
(A) | the motion of the gas molecules freezes at \(0^\circ\text C.\) |
(B) | the mean free path of gas molecules decreases if the density of molecules is increased. |
(C) | the mean free path of gas molecules increases if the temperature is increased keeping the pressure constant. |
(D) | \(\dfrac32k_B T\) (for monoatomic gases). | average kinetic energy per molecule per degree of freedom is
1. | (A) and (C) only |
2. | (B) and (C) only |
3. | (A) and (B) only |
4. | (C) and (D) only |
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