Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Two moles of an ideal gas is expanded isothermally and reversibly from 1 litre to 10 litres at \(300 \mathrm{~K}\). The enthalpy change (in \(\mathrm{kJ}\) ) for the process is [2004S] (a) \(11.4 \mathrm{~kJ}\) (b) \(-11.4 \mathrm{~kJ}\) (c) \(0 \mathrm{~kJ}\) (d) \(4.8 \mathrm{~kJ}\)

Step-by-Step Solution

Answer

The enthalpy change is (c) 0 kJ.

Step 1: Understand the Process

This is an isothermal (constant temperature) expansion of an ideal gas. During an isothermal process of an ideal gas, the internal energy change is zero.

Step 2: Recall Enthalpy Change Formula

For an ideal gas, the change in enthalpy ( ΔH) during a temperature change is given by ΔH = nC_pΔT. In an isothermal process (i.e., ΔT = 0), and with no change in internal energy, the enthalpy change, ΔH = 0.

Step 3: Conclusion of Entropy Change

Since the temperature remains constant and according to the enthalpy change formula for an isothermal process, the change in enthalpy is zero.

Key Concepts

Isothermal Expansion

In thermodynamics, an isothermal expansion refers to the process of a gas expanding at a constant temperature. This means that while the volume of the gas increases, the temperature does not change. As a consequence, the internal energy of an ideal gas remains constant because internal energy depends only on temperature. An ideal gas that undergoes an isothermal expansion does work on its surroundings because energy is transferred to the environment as the gas expands and the volume increases.

• Constant temperature: The process happens without changing the gas's temperature.
• Volume increase: The gas occupies more space, raising its volume.
• Energy and work: The heat energy absorbed by the gas is equal to the work done by the gas expanding.

This property effectively means that even though the gas molecules move further apart, the overall energy state of the gas remains unchanged.

Enthalpy Change

Enthalpy change, often symbolized as ΔH, measures the total heat content of a system. It is especially relevant in chemical reactions and processes like gas expansions or compressions. For an ideal gas, the formula for enthalpy change is ΔH = nC_pΔT, where:

• ΔH is the enthalpy change.
• n is the number of moles of the gas.
• C_p is the heat capacity at constant pressure.
• ΔT is the temperature change.

In the case of isothermal processes, like the one in our exercise, ΔT equals zero. As a result, the change in enthalpy (ΔH) is also zero.

This concept highlights an important aspect of isothermal processes: no heat content changes within the system, emphasizing that no heat is "stored" or "lost" in these types of expansions.

Thermodynamics

Thermodynamics is the branch of physics concerned with heat, work, and energy transformations. It provides principles that dictate how energy flows within a system and its surroundings, applying fundamental laws like the first and second laws of thermodynamics. The exercise involving isothermal expansion of an ideal gas relates closely to thermodynamic principles, especially the first law.

Key principles include:

• The first law, which is essentially the law of energy conservation, stating that energy cannot be created or destroyed.
• The second law, which introduces the concept of entropy, often interpreted as the level of disorder or randomness.

Understanding thermodynamics allows us to predict and calculate the behavior of gases during processes like expansion or compression. It is through these principles that we can evaluate the isothermal expansion without worrying about the change in the heat content or internal energy.

Reversible Process

A reversible process in thermodynamics refers to an idealized process that happens in such a way that the system and surroundings can be restored completely to their original states. In reality, most natural processes are irreversible, but considering reversible processes allows for simplified models by assuming no energy is dissipated due to friction, turbulence, or other inefficiencies.

Characteristics of a reversible process:

• Equilibrium: The system remains in thermodynamic equilibrium throughout the process.
• Infinitesimal changes: Changes occur so slowly and gradually that the system adjusts to equilibrium at every step.
• No entropy production: The entropy of the system remains constant.

In the context of the isothermal expansion, if it is also reversible, the gas does maximum work on its surroundings. This theoretical concept helps us evaluate the limits and potential efficiencies in industrial processes and everyday applications.