Question

What are the four processes that make up the Carnot cycle?

Short answer

Answer: The four processes that make up the Carnot cycle are: 1. Isothermal Expansion: The working substance expands at a constant temperature, receiving heat from a high-temperature source and doing work on the piston. 2. Adiabatic Expansion: The substance further expands without heat exchange, leading to a decrease in temperature while continuing to do work on the piston. 3. Isothermal Compression: The working substance is compressed at a constant temperature, releasing heat to a low-temperature sink and having work done on it by the piston. 4. Adiabatic Compression: The substance is further compressed without heat exchange, leading to an increase in temperature while work is done on it by the piston. The cycle can then repeat for continuous engine operation.

Step-by-step solution

Process 1: Isothermal Expansion

In the first process of the Carnot cycle, the working substance (usually a gas) undergoes isothermal expansion. This means that the temperature of the substance remains constant as it expands within the engine's cylinder. During this process, the working substance receives heat from a high-temperature source (usually denoted as \(T_{1}\)) and does work on the piston.

Process 2: Adiabatic Expansion

The second process in the Carnot cycle is adiabatic expansion. In this stage, the working substance further expands without gaining or losing heat; therefore, no heat exchange occurs with the surroundings. This process leads to a decrease in the substance's temperature until it reaches its lowest temperature (generally represented as \(T_{2}\)). The gas continues to do work on the piston during this process.

Process 3: Isothermal Compression

During the third process of the Carnot cycle, the working substance experiences isothermal compression. The temperature of the substance remains constant as it's compressed in the cylinder. During this step, the substance releases heat to a low-temperature sink (\(T_{2}\)), and work is being done on the substance by the piston.

Process 4: Adiabatic Compression

The fourth and final process in the Carnot cycle is adiabatic compression. Similar to adiabatic expansion, this step has no heat exchange between the working substance and its surroundings. The substance is further compressed, leading to an increase in its temperature back to the initial high temperature (\(T_{1}\)). In this stage, work is also performed on the substance by the piston. Once this process is complete, the cycle can repeat, maintaining the engine's continuous operation.