# Choose the option that most accurately represents the following statement:A heat engine absorbs 1800 kJ of heat from a hot body and rejects 600 kJ of heat to a cold sink. What is the heat engine's efficiency?

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1. 33.37
2. 66.67
3. 100
4. 50

Option 2 : 66.67
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## Detailed Solution

Concept:

• Carnot engine is a theoretical engine that operates on an ideal theoretical cycle called the Carnot cycle
• The efficiency of a heat engine is defined as the ratio of work output divided by heat input and is given by

$$η = 1 - \frac{T_{2}}{T_{1}}$$ or $$η = 1 - \frac{Q_{2}}{Q_{1}}$$

Where T2 =Temperature of the sink, T1= Temperature of the source, Q1 = Heat absorbed from the source, Q2= Heat rejected to the sink

Calculation:

Given:

Q1 = 1800 kJ and Q2 = 600 kJ

• The efficiency of the heat engine is given by

$$\Rightarrow η = 1 - \frac{Q_{2}}{Q_{1}}$$

Substituting the given values in the above equation

$$\Rightarrow η = 1 - \frac{6000}{1800}=1-\frac{1}{3}=\frac23=0.67$$
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