Question

Devise a Carnot heat engine using steady-flow components, and describe how the Carnot cycle is executed in that engine. What happens when the directions of heat and work interactions are reversed?

Short answer

Based on the given step-by-step solution, answer the following question: Question: Describe the four processes of a Carnot heat engine using steady-flow components and explain what occurs when the direction of heat and work interactions is reversed. Answer: A Carnot heat engine using steady-flow components consists of four processes: 1) Isothermal heat addition (HX1) - The working fluid absorbs heat Q_in from a high-temperature reservoir while maintaining temperature T1. 2) Adiabatic reversible expansion (N1) - The fluid expands adiabatically in the nozzle, decreasing its temperature and pressure from T1 to T2, and increasing its kinetic energy with work output. 3) Isothermal heat rejection (HX2) - The fluid rejects heat Q_out to a low-temperature reservoir while maintaining temperature T2 constant. 4) Adiabatic reversible compression (D1) - The fluid is compressed in the diffuser, increasing its pressure and temperature from T2 to T1 without heat interaction. When the direction of heat and work interactions is reversed, the Carnot heat engine becomes a Carnot refrigerator. The work is done on the fluid to transfer heat from a low-temperature reservoir to a high-temperature reservoir, and the processes and their order are reversed. The total work input is equal to the difference between the heats added and rejected.

Step-by-step solution

1. Devise a Carnot heat engine using steady-flow components

A Carnot heat engine using steady-flow components can be represented through the following devices: - Reversible heat exchanger (HX1) designed to add heat (Q_in) isothermally at temperature T1. - Reversible adiabatic nozzle (N1) to expand the fluid without heat interaction (from T1 to T2). - Reversible heat exchanger (HX2) designed to reject heat (Q_out) isothermally at temperature T2. - Reversible adiabatic diffuser (D1) to compress the fluid without heat interaction (from T2 to T1). This arrangement forms a closed loop, and each device corresponds to one part of the Carnot cycle.

2. Isothermal Heat Addition (HX1)

The working fluid enters HX1 at condition 1 with temperature T1 and absorbs heat Q_in from a high-temperature reservoir while maintaining the temperature T1. This is the first isothermal process in the Carnot cycle, and HX1 represents it.

3. Adiabatic Reversible Expansion (N1)

The hot working fluid from HX1 enters the nozzle N1 at condition 2, where it expands adiabatically in a reversible manner. The temperature and pressure of the fluid decrease from T1 to T2, and kinetic energy of the fluid increases with a corresponding work output. This process represents the adiabatic reversible expansion in the Carnot cycle.

4. Isothermal Heat Rejection (HX2)

The working fluid from N1 enters HX2 at condition 3 at temperature T2. The fluid rejects an amount of heat Q_out to a low-temperature reservoir while maintaining the temperature T2 constant. This is the second isothermal process in the Carnot cycle, represented by HX2.

5. Adiabatic Reversible Compression (D1)

The working fluid from HX2 is compressed in the diffuser D1 at condition 4, where the pressure and temperature increase from T2 to T1 without heat interaction. This process represents the adiabatic reversible compression in the Carnot cycle.

6. Reversed Heat and Work Interactions

When the directions of heat and work interactions are reversed, the Carnot heat engine becomes a Carnot refrigerator. In this case, the work is done on the fluid to transfer heat from a low-temperature reservoir to a high-temperature reservoir, following an opposite cycle. The processes and their order are reversed, and the total work input is now equal to the difference between the heats added and rejected.