# Carnot Engine ~ Electric Generating station

• Coti1002
In summary, an electric generating station is designed to have an electric output power of 1.4 MW, using a turbine with two-thirds efficiency of a Carnot engine. The Exhaust energy is transferred by heat to a cooling tower at 110°C. The efficiency of the engine as a function of Th and Tc is unknown, but is listed in the book as Qc/Δt=1.4((.5Th+383)/(Th-383)) which can be found using the 1st law. The actual Qh and therefore actual Qc is found by solving for Qc using Qh-Qc and the work output dW/dt=1.4MW.
Coti1002

## Homework Statement

An electric generating station is designed to have an electric output power of 1.4 MW using a turbine with two-thirds efficiency of a Carnot engine. The Exhaust energy is transferred by heat to a cooling tower at 110°C.

a) Find the rate at which the station exhausts energy by heat as a function of the fuel combustion temperature Th

## Homework Equations

e= w/Qh=1-Qc/Qh , e_carnot=1-Tc/Th, P=W/t

## The Attempt at a Solution

The only thing i have been able to figure out so far is e=(2/3)(1-(Tc/Th) Where Tc=383K

I have been struggling with this one for quite some time and humbly asking for your help

The book lists the answer as Qc/Δt=1.4((.5Th+383)/(Th-383))
I am so confused...

Book is right.

What is the efficiency of a Carnot engine as a function of Th and Tc? Then, what is actual Qh and therefore actual Qc? Hint: use 1st law.

I'm Sorry I'm still not following you...

Man I feel like an idot.. What am i missing?

Last edited:
Coti1002 said:

## Homework Statement

An electric generating station is designed to have an electric output power of 1.4 MW using a turbine with two-thirds efficiency of a Carnot engine. The Exhaust energy is transferred by heat to a cooling tower at 110°C.

a) Find the rate at which the station exhausts energy by heat as a function of the fuel combustion temperature Th

## Homework Equations

e= w/Qh=1-Qc/Qh , e_carnot=1-Tc/Th, P=W/t

## The Attempt at a Solution

The only thing i have been able to figure out so far is e=(2/3)(1-(Tc/Th) Where Tc=383K

I have been struggling with this one for quite some time and humbly asking for your help

The book lists the answer as Qc/Δt=1.4((.5Th+383)/(Th-383))
I am so confused...
If the output power is 1.4 MW what is the rate at which energy is input? Hint: efficiency = output/input = (dW/dt)/(dQh/dt)

Once you get the rate of energy input, given the work output dW/dt = 1.4MW you can calculate the rate of exhaust energy Qc using W = Qh-Qc (i.e. dW/dt = dQh/dt - dQc/dt).

Since efficiency is a function of Th (Tc=110C) you will have a Th in your answer. Be sure to use the Kelvin scale for T.
AM

Last edited:
Coti1002 said:
I'm Sorry I'm still not following you...

Man I feel like an idot.. What am i missing?

<<What is the efficiency of a Carnot engine as a function of Th and Tc? Then, what is actual Qh and therefore actual Qc? Hint: use 1st law. >>Try to answer those two questions! The first is in your textbook. Call it e.

Then, what does the 1st law say? How about Qh = Qc + W?
For your system, efficiency = 2e/3 = e' so write Qh in terms of W and e'( Th, Tc).
Then, solve for Qc. Realize that the answer to your problem is dQc/dt which will be in terms of dW/dt = P = 1.4MW as well as Th and Tc.

I can say no more.

## 1. What is a Carnot Engine?

A Carnot Engine is a theoretical engine that operates on the reversible Carnot cycle, which is the most efficient thermodynamic cycle for converting heat energy into mechanical work. It is named after French physicist Nicolas Léonard Sadi Carnot.

## 2. How does a Carnot Engine work?

A Carnot Engine works by absorbing heat energy from a high temperature source, converting some of it into mechanical work, and rejecting the remaining heat energy to a low temperature sink. This process is repeated in a cycle to produce continuous work.

## 3. What is the efficiency of a Carnot Engine?

The efficiency of a Carnot Engine is given by the formula: efficiency = (T high - T low) / T high, where T high is the temperature of the high temperature source and T low is the temperature of the low temperature sink. This means that the efficiency of a Carnot Engine is dependent on the temperature difference between the two sources.

## 4. What is the purpose of an Electric Generating Station?

An Electric Generating Station is a facility that converts various forms of energy (such as mechanical, chemical, nuclear, or solar) into electrical energy. This energy can then be distributed to homes, businesses, and other facilities for use.

## 5. How are Carnot Engines used in Electric Generating Stations?

Carnot Engines are not typically used in Electric Generating Stations. However, the principles of the Carnot cycle are used in the design of more efficient power plants, such as combined cycle power plants, which use both gas and steam turbines to generate electricity. Additionally, some renewable energy sources such as geothermal power plants operate on a modified Carnot cycle.

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