# Heat Engines and the Carnot Cycle

• HELLO11
In summary, To find Tc for a Carnot engine with an efficiency of 15%, you can use the equation e = 1 - \frac{Tc}{Th} = 1 - \frac{Tc}{Tc+55}, setting e to 0.15 and solving algebraically. The first step would be \frac{Tc}{Tc+55} = 1 - 0.15 = 0.85.
HELLO11
[SOLVED] Heat Engines and the Carnot Cycle

## Homework Statement

The operating temperatures for a Carnot engine are Tc and Th= Tc + 55K. The efficiency of the engine is 15%.

How do i find Tc?

$$e = 1 - \frac{Tc}{Th} = 1 - \frac{Tc}{Tc+55}$$

One equation one unknown should not be a problem...

Thats all mastering physics gives me. A problem like that is in the book but the efficiency of the engine is 11% instead. They get 450 K for Tc

Keep in mind that while efficiencies are often quoted as percentages, they must be used in equations as fractions. Set e = 0.15 and you should be able to solve the Carnot equation for Tc.

Do i set e= 0.15 to the equation above? and if i do how do i go about getting the answer?

HELLO11 said:
Do i set e= 0.15 to the equation above?

That's correct.

and if i do how do i go about getting the answer?

You will have to re-arrange the equation algebraically. Starting from

$$0.15 = 1 - \frac{Tc}{Tc+55}$$ , the first step would be

$$\frac{Tc}{Tc+55} = 1 - 0.15 = 0.85$$

thanks for the help

## 1. What is a heat engine?

A heat engine is a device that converts heat energy into mechanical work. It operates by using a temperature difference to drive a cyclic process that produces work.

## 2. What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat energy into mechanical work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

## 3. How does a heat engine work?

A heat engine works by using the temperature difference between a hot reservoir and a cold reservoir to drive a cyclic process. This process involves the transfer of heat from the hot reservoir to the working fluid, which then expands and does work on the surroundings. The remaining heat is then rejected to the cold reservoir, completing the cycle.

## 4. What is the efficiency of a Carnot cycle?

The efficiency of a Carnot cycle is the ratio of the work output to the heat input. It is given by the formula: Efficiency = (Temperature of hot reservoir - Temperature of cold reservoir) / (Temperature of hot reservoir).

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

Heat engines are used in a variety of real-life applications, including car engines, steam turbines, and gas turbines. They are also used in power plants to generate electricity from fossil fuels, nuclear energy, and renewable sources such as solar and geothermal energy.

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