Problem 135 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) Reversible cooling of an ideal gas at constant volume (b) Reversible isothermal expansion of an ideal gas (c) Adiabatic expansion of non-ideal gas into vaccum. (d) Reversible melting of sulphur at normal melting point. Column-II (p) \(\mathrm{w}=0, \mathrm{q}<0, \Delta \mathrm{U}<0\) (q) \(\mathrm{w}=0, \mathrm{q}>0, \Delta \mathrm{U}>0\) (r) \(\mathrm{w}=0, \mathrm{q}=0, \Delta \mathrm{U}=0\) (s) \(\mathrm{w}<0, \mathrm{q}>0, \Delta \mathrm{U}=0\) (t) \(\Delta \mathrm{H} \neq 0\)

Step-by-Step Solution

Answer

(a)-(p), (b)-(s), (c)-(r), (d)-(t)

Step 1: Identify the Process for Each Case

Understand the thermodynamic process described in each part of Column-I. 1. (a) Reversible cooling of an ideal gas at constant volume means no work done (as volume is constant) and internal energy decreases as temperature decreases, so heat flow out must also be negative. 2. (b) Reversible isothermal expansion of an ideal gas implies the internal energy stays constant while heat absorbed is equal to work done by the system since the temperature is constant. 3. (c) Adiabatic expansion into a vacuum (Joule expansion) is a free expansion, meaning no work is done, no heat is exchanged, and the internal energy remains the same. 4. (d) Reversible melting is a phase change that occurs at constant temperature, and heat absorbed is equal to the change in enthalpy.

Step 2: Match with Column-II

Match the observations from each process to the given statements in Column-II. 1. For (a) Reversible cooling at constant volume: There is no work done (w=0), heat flow is out of the system (q<0), internal energy decreases (ΔU<0). This matches with (p). 2. For (b) Reversible isothermal expansion: Work is done (w<0), heat is absorbed (q>0), and internal energy change is zero (ΔU=0). This matches with (s). 3. For (c) Adiabatic expansion into vacuum: No work done (w=0), no heat exchange (q=0), and internal energy change is zero (ΔU=0). This matches with (r). 4. For (d) Reversible melting of sulphur: The process entails a heat change, corresponding to change in enthalpy (ΔH≠0). This matches with (t).

Key Concepts

Reversible Processes

Reversible processes in thermodynamics are idealized processes that occur so slowly that the system remains in constant equilibrium with its surroundings. Essentially, changes in the system are reversed if the process is carried out in the opposite direction, with no increase in entropy for the universe. This means the process is both efficient and theoretically attainable, although in practice, it is nearly impossible to achieve a truly reversible process. Key characteristics include:

• The system is always at equilibrium.
• Entropy change is minimal or zero when considering both the system and the surroundings.
• Any energy changes in the system are compensated by energy exchanges with the surroundings, such that the overall energy is conserved.

Understanding reversible processes is crucial because they serve as a benchmark against which the efficiency of real-world processes is measured.

Isothermal Expansion

Isothermal expansion refers to the expansion of a gas at a constant temperature. During this process, the system must exchange heat with its surroundings to maintain a constant temperature. This can occur in a reversible manner in a perfectly controlled environment. As the gas expands, it performs work on its surroundings by pushing back against external pressure. To maintain the temperature constant, heat is absorbed from the surroundings. The key points of isothermal expansion include:

• Temperature (T) remains constant.
• Internal energy (U) doesn't change because it depends only on temperature for an ideal gas.
• Heat (q) absorbed is equal to the work (w) done by the gas. In terms of equations, we have: q = w.

Such processes are often theoretically ideal and difficult to achieve in real-life applications, yet they help provide clarity into the study of gas behaviors and thermodynamic cycles.

Adiabatic Expansion

Adiabatic expansion is a process in which a gas expands without exchanging heat with its surroundings. Instead, the gas uses its own internal energy to perform work, leading to a change in temperature. In an adiabatic process, the system is perfectly insulated from its surroundings ensuring that no heat (q=0) flows in or out of the system. For an ideal adiabatic expansion, the internal energy decreases, causing the gas to cool as it performs work. Important aspects to remember about adiabatic expansion are:

• No heat is exchanged (q=0).
• The temperature of the system decreases as it does work on the surroundings.
• Internal energy decreases as the work is done by the system.

Adiabatic processes are particularly significant in natural systems where insulation is approximated, such as the atmosphere.

Phase Change

A phase change occurs when a substance transitions from one state of matter to another, such as from solid to liquid or liquid to gas. This process can be reversible if it occurs at the melting point or boiling point, under equilibrium conditions. During a phase change, heat energy is absorbed or released without changing the temperature of the system. Phase changes include processes like melting, freezing, vaporization, and condensation. Importantly, during these changes, the structure of the substance's particles transforms, which necessitates an energy change termed enthalpy change (H). For example, the reversible melting of sulfur involves the absorption of heat, corresponding to an enthalpy change that maintains constant temperature throughout the process. Feathered facts about phase changes:

• Temperature remains constant during the transition.
• The enthalpy change (H) is associated with overcoming intermolecular forces.
• The phase transition occurs at distinct amounts of required energy for different substances.

Understanding phase changes is necessary for grasping concepts in both chemistry and physics, as they are fundamental to various natural and industrial processes.