# How Do Carnot's Efficiency Formulas for Heat Engines Align?

• Tulio Cesar
In summary, the efficiency of a heat engine according to the Carnot cycle can be expressed as 1 - T2/T1, where T2 is the temperature of the cold source and T1 is the temperature of the hot source. This means that a higher T2 for the same T1 will result in a lower efficiency for the engine. However, the other formula (1 - Q2/Q1) can be confusing because a larger temperature results in less heat being exchanged with the cold source, while a lower temperature results in more heat being exchanged with the hot source. This contradiction can be explained by the gas laws, which show that heat energy is proportional to absolute temperature (T). Therefore, the expressions Q in the formula can
Tulio Cesar
My question is: according to Carnot cycle, the maximum efficiency of a heat engine is given by 1 - T2/T1, where T2 is the temperature of the cold source and T1 the temperature of the hot source. So, accordingly, as higher T2 is for a same T1, lowest is the efficiency of the engine. But, the other formula for efficiency (1 - Q2/Q1), gets me confuse because as bigger temperature is, minus heat is exchanged with the cold source, and as lower temperature is, more heat is exchanged with de hot source. I don't know if I missed any point but these two formulas seem contradictory for me.

The analysis of heat engines centres around the expansion of gases. It is possible to show that the work (energy) involved in compressing or expanding gases is give by P x V ,( area under P~ V graph or ∫P.dV ).
From the gas laws it is possible to show that P x V ∝ T.
This means that heat energy is proportional to Absolute temp (T) and therefore the expressions Q in your equation can be replaced by T

## 1. What is the definition of a heat engine?

A heat engine is a device that converts heat energy into mechanical work, typically through the use of a working fluid and a cycle of heat transfer and expansion.

## 2. How does a heat engine work?

A heat engine works by taking in heat energy from a hot source, using it to do mechanical work, and then releasing the remaining heat to a colder sink. This process repeats in a cycle, with the working fluid being continuously cycled through the engine.

## 3. What is the efficiency of a heat engine?

The efficiency of a heat engine is the ratio of the work output to the heat input. It is expressed as a percentage and is always less than 100%. The theoretical maximum efficiency of a heat engine is determined by the Carnot cycle and depends on the temperature of the hot and cold reservoirs.

## 4. What is the difference between a heat engine and a heat pump?

A heat engine converts heat energy into mechanical work, while a heat pump uses mechanical work to transfer heat from a colder source to a hotter sink. In other words, a heat engine creates work by moving heat, while a heat pump moves heat by using work.

## 5. What are some real-world applications of heat engines?

Heat engines are used in a variety of everyday devices, such as car engines, power plants, and refrigerators. They are also used in industrial processes, such as in the production of electricity and in chemical reactions. Additionally, heat engines play a crucial role in many natural processes, such as the water cycle and the Earth's climate system.

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