The Reversible Heat Engine

The reversible heat engine operates between two systems at constant temperatures of 600°C and 40°C. This means that the engine absorbs heat at 600°C and rejects heat at 40°C. The heat transfer to the engine is given as 2000 kJ.

The net work output of the combined engine-refrigerator is 350 kJ. This implies that the heat engine produces 350 kJ of work while also transferring 2000 kJ of heat to the refrigerator.

The Reversible Refrigerator

The reversible refrigerator operates between systems at constant temperatures of 40°C and -20°C. This means that the refrigerator absorbs heat at 40°C and rejects heat at -20°C. The goal of the refrigerator is to transfer heat from a lower temperature system (40°C) to a higher temperature system (-20°C), which is against the natural flow of heat.

Heat Transfers Involving the Refrigerator

To evaluate the heat transfers involving the refrigerator, we need to consider the energy balance equation for the combined engine-refrigerator system:

Net Work Output = Heat Transfer to the Engine - Heat Transfer from the Refrigerator

Given that the net work output is 350 kJ and the heat transfer to the engine is 2000 kJ, we can rearrange the equation to solve for the heat transfer from the refrigerator:

Heat Transfer from the Refrigerator = Heat Transfer to the Engine - Net Work Output
= 2000 kJ - 350 kJ
= 1650 kJ

Therefore, the heat transfer from the refrigerator is 1650 kJ.

Explanation

The reversible heat engine absorbs heat at a higher temperature (600°C) and rejects heat at a lower temperature (40°C). This temperature difference allows the engine to convert some of the absorbed heat into work. The net work output of the engine is 350 kJ.

The reversible refrigerator, on the other hand, operates in the opposite direction. It absorbs heat from a lower temperature system (40°C) and rejects heat to a higher temperature system (-20°C). This is achieved by doing work on the refrigerant, which extracts heat from the low-temperature system and transfers it to the high-temperature system.

In the combined engine-refrigerator system, the heat transfer to the engine is 2000 kJ, which is the heat absorbed at 600°C. The net work output of 350 kJ is produced by the engine. Therefore, the remaining heat transfer from the refrigerator can be calculated as the difference between the heat transfer to the engine and the net work output.

The heat transfer from the refrigerator is 1650 kJ, indicating that the refrigerator is responsible for transferring this amount of heat from the low-temperature system (40°C) to the high-temperature system (-20°C).

Conclusion

In the given scenario, the reversible heat engine operates between systems at temperatures of 600°C and 40°C. The reversible refrigerator operates between systems at temperatures of 40°C and -20°C. The heat transfer from the refrigerator is found to be 1650 kJ, based on the net work output of 350 kJ and the heat transfer to the engine of 2000 kJ. The refrigerator plays a crucial role in transferring heat against the natural flow, from the low-temperature system to the high-