High School Physics : Understanding Heat Engines

Study concepts, example questions & explanations for High School Physics

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Example Questions

Example Question #1 : Heat

A Carnot Cycle operates using a heat reservoir at a temperature of \(\displaystyle 200^oC\) and a cold reservoir at a temperature of \(\displaystyle 50^oC\). What is the operating efficiency, \(\displaystyle \eta\), of this cycle, to the nearest percent? 

Possible Answers:

\(\displaystyle 54\%\)

\(\displaystyle 26\%\)

\(\displaystyle 32\%\)

\(\displaystyle 75\%\)

Correct answer:

\(\displaystyle 32\%\)

Explanation:

The efficiency of a Carnot Cycle is defined by:

\(\displaystyle \eta = 1- \frac{T_C}{T_H}\)

In this calculation, temperatures are given in Kelvin. Since Celsius and Kelvin exist in a one-to-one ratio, a conversion is unnecessary unless desired. We will perform the conversion, since most classes will advise it.

\(\displaystyle K=^oC+273\)

\(\displaystyle 200^oC+273=473K,\ 50^oC+273=323K\)

Using these values, we can calculate the efficiency:

\(\displaystyle \eta=1-\frac{T_C}{T_H}=1-\frac{323K}{473K}=1-(0.683)=0.317\)

Convert this value to a percentage:

\(\displaystyle 0.317\times 100\%=31.7\%\approx32\%\)

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