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. | \(\frac{1}{2} R T\) average energy per mole. | Each degree of freedom is associated with
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 to \(6\) 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. |
1. | statement A only |
2. | statement A and C only |
3. | statement B and D only |
4. | statement B only |
A. | the motion of the gas molecules freezes at \(0^\circ \mathrm{C}.\) |
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. | \({3 \over 2}\mathrm k_\mathrm{B} \mathrm T\) (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) | \(\frac13nm\bar v^2\) |
(B) | the pressure exerted by an ideal gas | (Q) | \( \sqrt{\frac{3 R T}{M}} \) |
(C) | the average kinetic energy of a molecule | (R) | \( \frac{5}{2} R T \) |
(D) | the total internal energy of 1 mole of a diatomic gas | (S) | \(\frac32k_BT\) |
(A) | (B) | (C) | (D) | |
1. | (Q) | (P) | (S) | (R) |
2. | (R) | (Q) | (P) | (S) |
3. | (R) | (P) | (S) | (Q) |
4. | (Q) | (R) | (S) | (P) |
A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ~\mathrm{C}?\) (\(R=8.31\) J mol–1 K–1)
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. | \({ }_{235} \mathrm{UF}_6\) | 2. | \({ }_{238} \mathrm{UF}_6\) |
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