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kemileywenMarine
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An engine with an input temperature of 755K and an exhaust temperature of 453K has the same efficiency as an engine that is 40% efficient. Is this true or false? I am having trouble

Verified Answer :

meerkat18

Efficiency is usually defined as a benefit divided by a cost. Or in terms of temperature:

e=1−T cold/T hot

Here, you are given both temperatures, so you just need to plug them in, and then compare to 40%. You will get a decimal for 'e', so you'll have to multiply by 100 to get a percentage.

Answer:

True

Explanation:

The efficiency of a heat engine is defined as the ratio of work done by the energy to the input energy.

It is given by

\(\eta = \frac{W}{Q_{1}}\)

Where, W is the work done and Q1 is the input heat.

\(\eta = 1-\frac{T_{2}}{T_{1}}\)

Where, T2 is the temperature of cold reservoir and T1 is the temperature of hot reservoir.

Here, T1 = 755 K and T2 = 453 K

So, efficiency = \(\eta =1-\frac{453}{755}\)

efficiency = 40 %

So, it is true.

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