How do you calculate the efficiency of a heat engine?

1 What is a heat engine?

A heat engine is a system that operates in a cycle between two reservoirs of different temperatures. The higher-temperature reservoir, or the heat source, provides heat to the engine, while the lower-temperature reservoir, or the heat sink, receives heat from the engine. The engine uses part of the heat input to do work on the surroundings, and the rest is rejected as waste heat. The work output can be used to drive a turbine, a piston, or any other mechanical device.

2 What is efficiency?

Efficiency is a measure of how much useful work a heat engine can produce from a given amount of heat input. It is defined as the ratio of the work output to the heat input, expressed as a percentage or a fraction. The higher the efficiency, the more work the engine can do with less heat input. However, no heat engine can have an efficiency of 100%, because some heat will always be lost to the environment.

3 What is the Carnot cycle?

The Carnot cycle is a theoretical model of a heat engine that operates with the maximum possible efficiency. It consists of four reversible processes: two isothermal processes, in which the temperature remains constant, and two adiabatic processes, in which no heat transfer occurs. The Carnot cycle is idealized and cannot be realized in practice, but it serves as a benchmark for comparing the performance of real heat engines.

4 How to calculate the Carnot efficiency?

The Carnot efficiency is the efficiency of a heat engine that operates on the Carnot cycle. It depends only on the temperatures of the heat source and the heat sink, and not on the specific details of the engine. The Carnot efficiency can be calculated by using the following formula: Carnot efficiency = 1 - (Tc/Th) where Tc is the temperature of the heat sink in Kelvin, and Th is the temperature of the heat source in Kelvin. The Carnot efficiency is always less than 1, and it decreases as the temperature difference between the reservoirs decreases.

5 How to calculate the actual efficiency?

The actual efficiency is the efficiency of a real heat engine that operates on a specific cycle. It depends on the heat input, the work output, and the heat loss of the engine. The actual efficiency can be calculated by using the following formula: Actual efficiency = (Work output/Heat input) where Work output is the net work done by the engine per cycle, and Heat input is the net heat supplied to the engine per cycle. The actual efficiency is always less than the Carnot efficiency, because real heat engines involve irreversible processes and frictional losses.

6 How to improve the efficiency?

The efficiency of a heat engine can be improved by increasing the temperature difference between the heat source and the heat sink, reducing the heat loss to the environment, and minimizing the friction and other irreversibilities in the engine. However, there are practical limitations and trade-offs involved in achieving these goals. For example, increasing the temperature of the heat source may require more fuel and cause more pollution, while reducing the temperature of the heat sink may require more cooling and consume more water. Therefore, the design and operation of a heat engine must balance the efficiency, the cost, and the environmental impact.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?