Carnot engine is

Options

A. 1. reversible engine
B. 2. operating between two temperatures `T_(1)` (source) and `T_(2)` (sink) have maximum efficiency
C. 3. consisting of two isothermal processes connected by two adiabatic processes
D. 4. all of these

Answer

### Step-by-Step Solution for the Question: "Carnot engine is..."

1. **Understanding the Carnot Cycle**: The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two temperature reservoirs. It consists of four processes: two isothermal processes and two adiabatic processes.

2. **PV Diagram Representation**:
- Draw a PV (Pressure-Volume) diagram.
- Label the points of the cycle: A (start), B (end of isothermal expansion), C (end of adiabatic expansion), and D (end of isothermal compression).
- The cycle moves from A to B (isothermal expansion), B to C (adiabatic expansion), C to D (isothermal compression), and D back to A (adiabatic compression).

3. **Reversible Process**:
- The Carnot cycle is a reversible process. This means that the system can return to its initial state without any net change in the surroundings.
- In the PV diagram, since the cycle returns to the starting point A after completing all processes, it confirms that the process is reversible.

4. **Operating Between Two Temperatures**:
- The Carnot engine operates between two temperature reservoirs: T1 (hot reservoir) and T2 (cold reservoir).
- During the isothermal processes (A to B and C to D), the temperatures remain constant at T1 and T2, respectively.

5. **Maximum Efficiency**:
- The efficiency of the Carnot engine is defined as the ratio of work done by the engine to the heat absorbed from the hot reservoir.
- The Carnot cycle achieves maximum efficiency because it is an ideal cycle that operates without any irreversibilities.

6. **Conclusion**:
- Based on the analysis of the Carnot cycle, we can conclude that all statements regarding the Carnot engine being a reversible process, operating between two temperatures, and consisting of two isothermal and two adiabatic processes are correct.
- Therefore, the correct answer is option D: all of the above.