Assertion (A): For gas molecules absolute zero temperature is not the temperature of zero energy.
Reason (R): Only the kinetic energy of the molecules is represented by temperature.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Concept: Temperature and molecular energy. Temperature is a direct measure of the average translational kinetic energy of molecules. While kinetic energy is minimal at 0 K, gas molecules can still have potential energy from intermolecular interactions. Thus,0 K is not zero total energy. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): The internal energy of a real gas is function of both, temperature and volume.
Reason (R): For any gas internal kinetic energy depends on temperature and internal potential energy depends on volume.
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 ideal gas, internal energy depends only on temperature. For a real gas, intermolecular forces exist, giving rise to internal potential energy in addition to kinetic energy. The internal kinetic energy depends on temperature, while the internal potential energy depends on the average distance between molecules, which is related to the volume. Thus, Assertion (A) is true, and Reason (R) is true. Reason (R) provides the accurate explanation for why the internal energy of a real gas is a function of both temperature and volume.
Assertion (A): Vibrational energy of molecule at temperature \(T\) is \(kT\).
Reason (R): For every molecule, vibrational degree of freedom is 2.
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
Assertion (A) is true as each vibrational mode contributes \(kT\) to the internal energy. Reason (R) is false; vibrational degrees of freedom vary by molecular structure (e.g., diatomic molecules have 1). Thus, (A) is true and (R) is false.
Assertion (A): A gas is kept in an insulated cylinder with a movable piston, in compressed state. As the piston is suddenly released, temperature of the gas decreases.
Reason (R): According to the kinetic theory of gas, a molecule colliding with the piston must rebound with less speed than it had before the collision. Hence average speed of the molecules is reduced.
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
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In an adiabatic expansion, the gas does work on the receding piston. Molecules lose kinetic energy upon collision, reducing their average speed and thus the gas temperature. Reason (R) correctly explains Assertion (A).
Assertion (A): When an ideal gas is heated in a rigid non conducting container then pressure becomes double if the temperature is doubled.
Reason (R): Both the frequency of collisions and momentum transferred per collision becomes \( \sqrt{2} \) times.
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
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Assertion (A) is true by ideal gas law \( P \propto T \) at constant volume. Reason (R) is also true, as \( v_{rms} \propto \sqrt{T} \), affecting both collision frequency and momentum transfer per collision by a factor of \( \sqrt{2} \) when T is doubled. (R) correctly explains (A).
Assertion (A): The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
Reason (R): The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
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
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Assertion (A) is true because \( E_k = \frac{3}{2} nRT \) and \( PV = nRT \), so \( E_k = \frac{3}{2} PV \). Reason (R) is also true, as molecules of an ideal gas undergo elastic collisions with each other, changing their individual velocities. However, (R) does not explain (A).
Assertion (A): According to kinetic theory of gases the internal energy of a given sample of an ideal gas is only kinetic.
Reason (R): The ideal gas molecules exert force on each other only when they collide.
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
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For an ideal gas, internal energy is purely kinetic due to random motion, so (A) is true. Ideal gas molecules have no intermolecular forces, so (R) is false. Thus, (A) is true and (R) is false.
Assertion (A): The specific heat of a monatomic gas may have value between \(0\) and \(\infty\).
Reason (R): \(C_p = \frac{5}{2} R\) and \(C_v = \frac{3}{2} R\) for a monatomic gas.
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
Assertion (A) is true; specific heat depends on the process and can range from \(0\) (adiabatic) to \(\infty\) (isothermal). Reason (R) is true; the specific heats for a monatomic gas are correctly given.
However, R provides specific values and does not explain the general range of specific heat values mentioned in A. Therefore, R is not the correct explanation of A.
Assertion (A): P-T graph of all gases at low density meet at \(0 K\).
Reason (R): Absolute zero kelvin is less than \(0^{\circ}C\) in Celsius scale.
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
Assertion (A) is true. Extrapolation of the P-T (isochoric) graphs for ideal gases shows they converge to zero pressure at \(0 K\). Reason (R) is true; \(0 K\) is equal to \(-273.15^{\circ}C\), which is indeed less than \(0^{\circ}C\). However, R is a statement about temperature scale conversion and does not explain the behavior of the P-T graph.
Assertion (A): An ideal gas has infinitely many molar specific heats.
Reason (R): Specific heat is amount of heat needed to raise the temperature of \(1\) mole of gas by \(1K\).
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
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Assertion (A) is true. An ideal gas can undergo various thermodynamic processes (isobaric, isochoric, adiabatic, polytropic, etc.), each associated with a unique specific heat capacity.
Reason (R) is true; it is the definition of molar specific heat. However, the definition does not explain *why* there are infinitely many such values; this stems from the different possible thermodynamic paths.