AIIMS 2003 Chemistry First Law of Thermodynamics Assertion Reason Question

To analyze the assertion and reasoning provided in the question, we need to explore both concepts of internal energy changes during vaporization and the principles of isothermal processes.

Assertion:

The increase in internal energy ($\Delta E$) for the vaporization of one mole of water at 1 atm and 373 K is zero.

Reason:

For all isothermal processes, $\Delta E = 0$.

Explanation:

1. Understanding the Assertion:

   • When water vaporizes at its boiling point (373 K) and at 1 atm, it transitions from the liquid phase to the gas phase. The process requires energy, known as the enthalpy of vaporization ($\Delta H_{vap}$).
   • However, when vaporization occurs at the boiling point under constant pressure, the system is in a state of equilibrium where the energy added to the system as heat (to vaporize the water) is balanced by the work done by the system expanding against the external pressure.
   • At this specific point, the change in internal energy ($\Delta E$) for the phase change can be expressed using the First Law of Thermodynamics, which states: $\Delta E = q - W$ where $q$ is the heat added to the system and $W$ is the work done by the system.
   • For the vaporization of water at constant temperature and pressure, the heat added ($q = \Delta H_{vap}$) is used to do work against the atmosphere ($W = P\Delta V$). Therefore, for phase changes at equilibrium (like vaporization), the net change in internal energy ($\Delta E$) can indeed be zero, making the assertion correct.

2. Understanding the Reason:

   • The reasoning states that for all isothermal processes, $\Delta E = 0$. This is not entirely accurate. While it is true that for certain isothermal processes (especially those involving ideal gases under specific conditions), the change in internal energy can be zero, it does not apply universally to all processes.
   • For example, in isothermal expansion of an ideal gas, $\Delta E$ is zero because internal energy for an ideal gas depends only on temperature. However, in other isothermal processes involving phase changes, such as vaporization, the internal energy may change depending on the system's work and heat interactions. Hence, while the reasoning holds for ideal gases, it does not extend to the assertion about water vaporization.

Conclusion:

• Since the assertion is true and the reasoning is not universally applicable, the correct answer is A (Assertion is true, Reason is false).

Incorrect Options:

• Option B: Assertion is true, Reason is true, but Reason is not a correct explanation of Assertion.
• Option C: Assertion is false, Reason is true; this is incorrect as the assertion is indeed true.
• Option D: Both Assertion and Reason are false; this is incorrect because the assertion is true.

Summary:

The assertion that the increase in internal energy for the vaporization of one mole of water at 1 atm and 373 K is zero is correct, as the heat added is balanced by the work done, leading to no net change in internal energy. However, the reasoning provided does not hold for all isothermal processes, making the assertion true while the reasoning is false. Therefore, the correct answer is A.