A steady-flow Carnot cycle uses water as the working fluid. The water changes from a saturated liquid to saturated vapor as heat is transferred to it from a source at 280◦C. Heat rejection takes place at a pressure of 200 kPa.
The correct answer and explanation is:
In the Carnot cycle, the working fluid undergoes two isothermal processes and two adiabatic processes. For this specific cycle, water is used as the working fluid. The process operates between a heat source at 280°C and a heat sink at 200 kPa pressure. The water transitions from a saturated liquid to a saturated vapor during the heat absorption process and rejects heat as it returns to the liquid phase.
Step 1: Heat Absorption (Isothermal Expansion)
The cycle begins by heat being transferred to the water at a high temperature (280°C). At this point, the water is in a saturated liquid state. During this phase, the temperature remains constant at 280°C as the water absorbs heat from the source and changes from a liquid to a vapor, without a change in temperature. This is called the isothermal expansion phase. The water reaches a saturated vapor state by the end of this phase.
Step 2: Adiabatic Expansion
After the water has become saturated vapor, the cycle continues with an adiabatic expansion process, during which the water does not exchange heat with its surroundings, but does perform work on the surroundings (for example, moving a piston). As the water expands, its pressure and temperature decrease. This expansion happens without heat exchange and is governed by the thermodynamic relationships for adiabatic processes.
Step 3: Heat Rejection (Isothermal Compression)
Next, heat rejection occurs at a constant temperature, but at a lower pressure of 200 kPa. The water, now a vapor, is compressed isothermally, transferring heat to the heat sink at this lower pressure. The temperature remains constant during this phase, but the volume decreases as the water compresses into the liquid phase.
Step 4: Adiabatic Compression
Finally, the cycle concludes with an adiabatic compression, where the water is compressed further without heat exchange, causing its temperature and pressure to rise again, returning the system to its initial state, ready to start the process over again.
This steady-flow Carnot cycle is efficient because the heat engine operates between two reservoirs at constant temperatures, extracting maximum work from the energy transferred. The efficiency of the cycle can be expressed using the Carnot equation, which depends on the temperatures of the hot and cold reservoirs.