Assertion (A): The ratio \( \frac{C_P}{C_V} \) is more for helium gas than for hydrogen gas.
Reason (R): Atomic mass of helium is more than that of hydrogen.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
For Helium (monoatomic), \( \gamma = 5/3 \). For Hydrogen (diatomic), \( \gamma = 7/5 \). Since \( 5/3 > 7/5 \), (A) is true. Atomic mass of He is 4 amu, H is 1 amu (H2 is 2 amu), so (R) is true.
However, \( \gamma \) depends on degrees of freedom (monoatomic vs diatomic), not atomic mass. So, (R) is not the correct explanation.
Assertion (A): On a V-T graph, the slope of an isobar increases with pressure.
Reason (R): At constant temperature, for an ideal gas its volume is directly proportional to its pressure.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
For an isobar, \( V = (\frac{nR}{P})T \). The slope on a V-T graph is \( \frac{nR}{P} \). As P increases, slope decreases, so (A) is false. Boyle's law states that at constant T, \( V \propto \frac{1}{P} \), i.e., V is inversely proportional to P, so (R) is false.
Assertion (A): Internal energy of real gas is always negative at absolute zero temperature.
Reason (R): Potential energy of a bounded system is negative.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
At absolute zero, kinetic energy is minimal (zero for ideal gas). For a real gas, attractive intermolecular forces mean potential energy is negative (relative to infinite separation). So, total internal energy is negative. Thus, (A) is true. (R) is also true, as attractive forces in a bounded system lead to negative potential energy. (R) explains (A).
Assertion (A): The average translational kinetic energy of the molecules in one mole of all ideal gases, at the same temperature is the same.
Reason (R): The average kinetic energy of one mole of any ideal gas at temperature T is given by \( \frac{3}{2}RT \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The average translational kinetic energy per mole for any ideal gas is \( \frac{3}{2}RT \), dependent only on T.
So (A) is true. The formula in (R) represents this average translational kinetic energy per mole. So (R) is true and correctly explains (A).
Assertion (A): For an ideal gas, at constant temperature, the product of the pressure and volume is constant.
Reason (R): The mean square velocity of gas molecules is inversely proportional to mass of molecule.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Boyle's Law states that for an ideal gas at constant T, \( PV = \text{constant} \). So (A) is true. The mean square velocity \( = \frac{3kT}{m} \), so it is inversely proportional to molecular mass m.
So (R) is true. However, (R) does not explain Boyle's law (A).