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Engine Efficiency (AQA A Level Physics)

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Ashika

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Ashika

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Engine Efficiency

  • The efficiency of an engine can be measured in three different ways: overall, thermal and mechanical 

  • The overall efficiency of an engine is:

o v e r a l l space e f f i c i e n c y space equals space fraction numerator space b r a k e space p o w e r space over denominator i n p u t space p o w e r end fraction

  • This is also the product of the thermal and mechanical efficiencies

  • The thermal efficiency of an engine is:

t h e r m a l space e f f i c i e n c y space equals space fraction numerator space i n d i c a t e d space p o w e r over denominator i n p u t space p o w e r end fraction

  • This tells us how well the engine transforms the chemical energy in the fuel into useful power (and work) in the engine cylinders

  • The mechanical efficiency engine is:

m e c h a n i c a l space e f f i c i e n c y space equals space fraction numerator space b r a k e space p o w e r over denominator i n d i c a t e d space p o w e r end fraction

  •  This depends on the amount of energy lost due to moving parts of the engine (due to friction)

Worked Example

An engine consumes fuel at the rate of 0.90 kg per second. The calorific value of the fuel is 44 MJ kg–1.

The indicated power of the engine is 4720 kW. Because of the high speed of the air in the engine, there is significant frictional heating amounting to a power loss of 230 kW. 

Calculate the overall efficiency of the engine.

Answer:

Step 1: State the overall efficiency equation

O v e r a l l space e f f i c i e n c y space equals space fraction numerator space b r a k e space p o w e r over denominator i n p u t space p o w e r end fraction

Step 2: Calculate the brake power

F r i c t i o n space p o w e r space space equals space i n d i c a t e d space p o w e r space minus space b r a k e space p o w e r

B r a k e space p o w e r space equals space i n d i c a t e d space p o w e r space minus space f r i c t i o n space p o w e r

B r a k e space p o w e r space equals space 4720 space minus space 230 space equals space 4490 space kW

Step 3: Calculate the input power

I n p u t space p o w e r space equals space c a l o r i f i c space v a l u e space cross times space f u e l space f l o w space r a t e

I n p u t space p o w e r space equals space space open parentheses 44 space cross times space 10 to the power of 6 close parentheses space cross times space 0.90 equals space 3.96 space cross times space 10 to the power of 7 space straight W

Step 4: Calculate the overall efficiency;

O v e r a l l space e f f i c i e n c y space equals space fraction numerator 4490 space cross times space 10 cubed space over denominator 3.96 space cross times space 10 to the power of 7 end fraction space equals space 0.11 space open parentheses 11 percent sign close parentheses

Examiner Tips and Tricks

These formulas are not given on your data sheet, so make sure to remember these!

You can see from the worked example that it's very important to understand how and when to use the power equations! 

Exam questions may be set on other theoretical cycles of other engines, which you don't need to know the working knowledge of. Therefore, the questions will be interpretive, so you should be confident in finding the area under a p-V loop for different engines or their efficiency.

You will also be examined on how well you understand what is going on in the engine based on the information given (they will not stray too far from diesel and petrol)

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.