Understanding Thermodynamic Processes and Characteristics

This question asks us to match different thermodynamic processes with their key characteristics. Understanding these processes is fundamental in thermodynamics.

Analyzing Each Process and Characteristic Match

Let's examine each process listed in List – I and find its corresponding characteristic from List – II.

1. Throttling process: A throttling process is typically an adiabatic process (no heat transfer) where a fluid flows through a restriction, like a valve or porous plug, without doing any work. A key characteristic of a throttling process is that the enthalpy remains constant. This is often seen in refrigeration cycles.
   • Matches with (iv) Constant enthalpy.
2. Isentropic process: An isentropic process is a reversible adiabatic process. By definition, an adiabatic process has no heat transfer ($\delta Q = 0$). A reversible process has no entropy generation. The entropy change ($\Delta S$) for a process is given by $\Delta S = \int \frac{\delta Q}{T} + S_{gen}$, where $S_{gen}$ is entropy generation. For a reversible adiabatic process, $\delta Q = 0$ and $S_{gen} = 0$, so $\Delta S = 0$. This means the entropy remains constant.
   • Matches with (ii) No change in entropy.
3. Free expansion: Free expansion is an irreversible process where a gas expands into a vacuum. There is no external work done because there is no opposing pressure ($W = \int P dV = 0$ since the external pressure is zero). If the system is isolated, it is also adiabatic ($Q=0$). According to Joule's law, for an ideal gas undergoing free expansion, the internal energy remains constant. However, option (iii) is Constant Internal energy and option (i) is No work done. Between these, "No work done" is a direct and general characteristic of free expansion, even for real gases expanding into a vacuum where internal energy might change slightly. For ideal gases, it is also constant internal energy. Comparing with the given options, "No work done" is the most direct match for free expansion as it happens against vacuum.
   • Matches with (i) No work done.
4. Isothermal process: An isothermal process is one that occurs at a constant temperature ($T$). For an ideal gas, the internal energy ($U$) depends only on temperature ($U = U(T)$). Therefore, if the temperature is constant, the internal energy is also constant ($\Delta U = 0$).
   • Matches with (iii) Constant Internal energy (for ideal gases).

Consolidating the Matches

• a. Throttling process – (iv) Constant enthalpy
• b. Isentropic process – (ii) No change in entropy
• c. Free expansion – (i) No work done
• d. Isothermal process – (iii) Constant Internal energy

Let's arrange these matches as required:

The correct combination is a – (iv), b – (ii), c – (i), d – (iii).

Final Answer Derivation

Comparing our derived matches with the given options, we find that:

• Option 1: a – (iv), b – (ii), c – (i), d – (iii)
• Option 2: a – (i), b – (ii), c – (iv), d – (iii)
• Option 3: a – (iv), b – (iii), c – (i), d – (ii)
• Option 4: a – (i), b – (iii), c – (iv), d – (ii)

Our derived combination matches Option 1 exactly.