# Energy Efficiency

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3.6 The Carnot Efficiency

The Carnot Efficiency is the theoretical maximum efficiency one can get when the heat engine is operating between two temperatures:

• The temperature at which the high temperature reservoir operates (Thot).

• The temperature at which the low temperature reservoir operates (Tcold).

In the case of an automobile, the two temperatures are:

• The temperature of the combustion gases inside the engine (Thot).

• The temperature at which the gases are exhausted from the engine (Tcold).

Can we show a car engine? Maybe animate it? YES Here’s one from http://auto.howstuffworks.com/engine1.htm Can we develop something similar?

The following may be best explained via audio and narration: When the exhaust is leaves the automobile at a higher temperature, it carries more energy out so that amount of energy is not available to be converted to work (moving piston). Therefore, we can conclude that the higher the Tcold, the lower the efficiency. Similarly, if the Thot is increased by increasing the temperature of the combustion gases, we can get higher efficiencies.
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Then, why should we operate the automobiles at low efficiencies?
It is not that we cannot achieve high temperatures, but we do not have the engine materials that can withstand the high temperature. As a matter of fact, we do not let the engine gases go the maximum that they can go even now and instead try to keep the engine cool by circulating the coolant.
So we are taking the heat out of the gases (thus lowering the Thot) and making the engine operate at cooler temperatures so that the engine is protected - but lowering the efficiency of an automobile.
More Information: It’s like Taxes. The more money you earn (heat), the more money is taxed (cold), leaving you with less money to take home (efficiency). However, if you could earn more money (heat) and find a way to have less taxes taken out (better engine material), you would have more money to take home (efficiency).

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Below are temperature ranges for the heat (hot) and exhaust (cold) of a car engine.

Using the scales above, enter several combinations of numbers for hot and cold, and observe the graph: (wants it to be like home simulations)

Hot

C
Efficiency

Function of 2 Temperatures
old

Based on your observations of the graph:

1. What happens as High T increases? Answer: Efficiency Increases

2. What happens as High T decreases? Answer: Efficiency decreases

3. What happens as Low T decreases? Answer: Efficiency increases

4. What happens as Low T increases? Answer: Efficiency decreases

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Illustration 3-3
For a coal-fired utility boiler, the temperature of high pressure steam would be about 540°C and Tcold, the cooling tower water temperature would be about 20°C. Calculate the Carnot efficiency of the power plant?
Solution:

Carnot efficiency depends on high temperature and low temperatures between which the heat engine operates. We are given both temperatures. However, the temperatures need to be converted to Kelvin

Thot = 540°C+273 = 813 K

Tcold = 20°C + 273 = 293 K

I need to find an example

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Vinit’s Problem 3-2

Example for equation 3.4

Illustration:

For a coal fired utility boiler, the temperature of high pressure steam would be about 540 degrees C and Tcold, the cooling tower water temperature would be about 20 degrees C. Calculate the Carnot efficiency of the power plant?

The solution............

Step 1: We are given the high temperature and the low temperatures between which the heat engine engine operates which is needed to calculate Carnot efficiency. To calculate, Convert the temperatures to Kelvin.
 Thot = 540 degrees C + 273 = 813 K Tcold = 20 degrees C + 273 = 293 K

Step 2: Use the formula for Carnot efficiency.
 Carnot Efficiency =(1 - Thot) x 100 Tcold =(1- 293 K) x 100 813 K = 64%

Why dont you give it a shot now....................

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For a coal fired utility boiler, the temperature of high pressure st

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3.7 Entropy and Quality of Energy

From the Carnot Efficiency formula, it can be inferred that a maximum of 64% of the fuel energy can go to generation. To make the Carnot efficiency as high as possible, either T hot should be increased or T cold (temperature of heat rejection) should be decreased.

Let’s look at the Energy conversions in a power plant: