For work done to be reversible, the process should be

Options

A. cyclic
B. isobaric
C. isochoric
D. adiabatic

Answer

To determine the conditions under which work done is reversible, we need to analyze the nature of different thermodynamic processes. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Reversibility
Reversible processes are idealized processes that can be reversed without leaving any change in the system or surroundings. For work done to be reversible, the system must return to its original state without any net change.

**Hint:** Reversibility implies that both the system and surroundings can be restored to their initial states.

### Step 2: Analyze the Work Done in Different Processes
The work done during a thermodynamic process can be expressed using the first law of thermodynamics:
\[ Q = \Delta U + W \]
where \( Q \) is the heat added to the system, \( \Delta U \) is the change in internal energy, and \( W \) is the work done.

**Hint:** The first law of thermodynamics helps us understand how energy is conserved during a process.

### Step 3: Consider Adiabatic Processes
In an adiabatic process, there is no heat exchange with the surroundings (\( Q = 0 \)). Therefore, the equation simplifies to:
\[ 0 = \Delta U + W \]
This implies:
\[ W = -\Delta U \]
In this case, all the work done on the system contributes to a change in internal energy, which can be fully recovered if the process is reversed.

**Hint:** An adiabatic process allows for the complete conversion of work into internal energy, making it reversible.

### Step 4: Contrast with Isothermal Processes
In an isothermal process, the temperature remains constant, which means:
\[ \Delta U = 0 \]
Thus, the equation becomes:
\[ Q = W \]
Here, heat is exchanged with the surroundings to maintain constant temperature. If the system loses heat, it cannot fully recover the work done because some energy has been dissipated.

**Hint:** In isothermal processes, heat exchange complicates the reversibility of work done.

### Step 5: Conclusion
For work done to be reversible, the process should be adiabatic. In an adiabatic process, there is no heat exchange, and the work done can be fully converted to internal energy, allowing for complete reversibility.

**Final Answer:** The process should be **adiabatic** for work done to be reversible.