# How Much Energy Does a Carnot Cycle Heat Engine Expel Per Cycle?

• S_fabris
JH In summary, in a Carnot cycle operating between temperatures of 354.05K and 711.15K, the heat engine absorbs 22415J of energy per cycle from the hot reservoir. The duration of each cycle is 0.98s. The mechanical power output is 11.49kW. The heat engine expels 11.16kJ of energy in each cycle by heat. This is calculated using Qc = Qh - W, where Qc represents the heat energy expelled to the cold reservoir. This is confirmed by the first law of thermodynamics, which states that W = Qh - Qc, and the efficiency of the Carnot cycle is given by \eta = 1 - \
S_fabris
Hey i have a heat engine that operates in a Carnot cycle between 354.05K and 711.15K, it absorbs 22415J of energy per cycle from hot resevoir. The duration of each cycle is 0.98s.
First question was to find the mechanical power output...i calculated this and got W = Qh - Qc = 22415 - 11159.43 = 11255.57 J/0.98s = 11,49kW

the next question asks how much energy does it expel in each cycle by heat in units of kJ..

everywhere I look it says to use Qc = Qh - W which gives me 11 159.43J is this right?? 11.16kJ?

this seems odd as an answer because it is the same answer as Qc.

Can anybody confirm this or steer me in right direction? thank you

S_fabris said:
Hey i have a heat engine that operates in a Carnot cycle between 354.05K and 711.15K, it absorbs 22415J of energy per cycle from hot resevoir. The duration of each cycle is 0.98s.
First question was to find the mechanical power output...i calculated this and got W = Qh - Qc = 22415 - 11159.43 = 11255.57 J/0.98s = 11,49kW

the next question asks how much energy does it expel in each cycle by heat in units of kJ..

everywhere I look it says to use Qc = Qh - W which gives me 11 159.43J is this right?? 11.16kJ?

this seems odd as an answer because it is the same answer as Qc.

Can anybody confirm this or steer me in right direction? thank you
! Qc IS the heat energy expelled in each cycle (ie the heat flowing to the cold reservoir.

For the Carnot cycle heat flows into and out of the reservoirs at constant temperature and there is 0 change in entropy. ie $\Delta S = Q_h/T_h - Q_c/T_c = 0$, so [itex]Q_c/Q_h = T_c/T_h[/tex]

From the first law: W = Qh - Qc, so

$$\eta = \frac{W}{Q_h} = \frac{Q_h - Q_c}{Q_h} = 1 - \frac{Q_c}{Q_h} = 1 - \frac{T_c}{T_h}$$

$$Q_c = Q_h\frac{T_c}{T_h}$$

AM

I can confirm that your calculation for the mechanical power output is correct. However, the calculation for the amount of energy expelled in each cycle by heat is incorrect. The correct equation to use is Qc = Qh - W, as you stated, but the value for Qc will not be the same as the value for Qh. Qc represents the amount of energy expelled by the heat engine to the cold reservoir, while Qh represents the amount of energy absorbed from the hot reservoir. In this case, Qc should be equal to 11,159.43 J, which is equivalent to 11.16 kJ. I would recommend double-checking your calculations to ensure accuracy. Additionally, it may be helpful to review the principles of the Carnot cycle to better understand the calculations involved.

## 1. What is a heat engine?

A heat engine is a device that converts heat energy into mechanical work. It operates by taking in heat from a high-temperature source, converting part of this heat energy into mechanical work, and then releasing the remaining energy to a low-temperature sink.

## 2. How does a heat engine work?

A heat engine works by using the principles of thermodynamics. It utilizes a working fluid, such as gas or liquid, to absorb heat energy from a hot source and expand. This expansion creates pressure, which in turn drives a piston or turbine to perform mechanical work. The remaining heat energy is then released to a cooler sink, and the cycle repeats.

## 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 typically measured as a percentage and is determined by the temperature difference between the hot and cold sources. The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency equation.

## 4. What is the purpose of a heat engine calculation?

A heat engine calculation is used to determine the efficiency and performance of a heat engine. It can also help in designing and optimizing heat engines for specific applications. Additionally, it can provide information on the amount of energy that can be converted into work by a heat engine.

## 5. What factors affect the performance of a heat engine?

The performance of a heat engine is affected by various factors, including the temperature difference between the hot and cold sources, the type of working fluid used, and the design and efficiency of the engine. Other factors such as friction, heat loss, and mechanical limitations can also impact the performance of a heat engine.

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