# Calculating Efficiency of Heat Engine with Steam in Saturation Dome

• Naeem
In summary: You could also use the enthalpy or the work divided by the temperature. I think that the maximum efficiency is reached when the engine works between the two extremes of the temperature table.
Naeem
Q. A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1 MPa during heat addition and 0.5 MPa during heat rejection. THe highest possible efficiency of the heat engine is.

How to calculate heat efficiency?

W = QH / COP,hp

and

COP = 1 / ( TH /TL - 1 )

Pl. note COP- denotes the coefficient of performance of the heat engine.

Any ideas on how to proceed?

Thanks, a lot!

Naeem said:
Q. A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1 MPa during heat addition and 0.5 MPa during heat rejection. THe highest possible efficiency of the heat engine is.

How to calculate heat efficiency?

W = QH / COP,hp

and

COP = 1 / ( TH /TL - 1 )

Pl. note COP- denotes the coefficient of performance of the heat engine.

Any ideas on how to proceed?

Thanks, a lot!

It seems to me that the engine is working with a Rankine Cycle. Anyway, during the change of state the pressure and temperature remains constant. If you have the pressure 1MPa then you have the temperature of saturation of water ($$T_h=180ºC=353K$$) and the pressure 0.5 Mpa gives you $$T_c=150ºC=323K$$ aproximately (verify the data in a table of water).

This means the engine, maybe an steam machine, is vaporizing water in the boiler at temperature $$T_h$$ which may be the hot focus (maybe it is not totally true in a Rankine cycle because the bolier superheats the vapor), and is condensing the vapor at temperature $$T_c$$ in the condenser. The second principle of the thermodynamics states than the maximum efficiency is reached by means of a Carnot engine working between the two extreme temperatures:

$$\eta_{max}=\frac{W}{Q_h}=1-T_c/T_h$$

I don't really understand why you used the COP when we are talking about an engine.

To calculate the efficiency of a heat engine with steam in the saturation dome, we can use the formula W = QH / COP,hp, where W is the work output, QH is the heat added, and COP,hp is the coefficient of performance of the heat engine.

To find the COP, we can use the formula COP = 1 / (TH/TL - 1), where TH is the temperature at which heat is added and TL is the temperature at which heat is rejected.

In this case, the pressure of the steam is given as 1 MPa during heat addition and 0.5 MPa during heat rejection. Using the steam tables, we can find the corresponding temperatures at these pressures.

Assuming that the heat engine is operating in a Carnot cycle, the highest possible efficiency would be given by the Carnot efficiency formula, which is 1 - TL/TH.

Therefore, to calculate the efficiency, we would need to first find the temperatures at the given pressures, then use the Carnot efficiency formula to find the highest possible efficiency.

I hope this helps! Let me know if you have any further questions or need clarification on any of the steps.

## 1. How do you define efficiency of a heat engine?

The efficiency of a heat engine is a measure of how effectively it converts heat energy into mechanical work. It is usually expressed as a percentage and is calculated by dividing the work output by the heat input.

## 2. What is a steam engine and how does it work?

A steam engine is a type of heat engine that uses steam as its working fluid. It works by heating water in a boiler to produce high pressure steam. The steam then moves through a series of pistons, pushing them and converting the heat energy into mechanical work.

## 3. How is the efficiency of a steam engine with steam in saturation dome calculated?

The efficiency of a steam engine with steam in saturation dome is calculated using the Carnot cycle. It involves measuring the heat input and work output at each stage of the cycle and then using the formula: efficiency = (work output/heat input) * 100%.

## 4. What factors can affect the efficiency of a steam engine?

The efficiency of a steam engine can be affected by various factors such as the design of the engine, the quality of the steam, the temperature and pressure of the steam, and the friction in the engine’s moving parts. Other external factors like ambient temperature and air resistance can also impact the engine’s efficiency.

## 5. How can the efficiency of a steam engine be improved?

To improve the efficiency of a steam engine, various measures can be taken such as optimizing the design of the engine, improving the quality of the steam, reducing friction, and minimizing heat loss. Regular maintenance and proper operation can also help in maintaining the efficiency of a steam engine.

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