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2nd Law of Thermodynamics

According to ...

Question

According to given figure which of the following options can be true ?

Q_{1}

Q_{2}

W

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In real aspects

Q_{2} = 0

always

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efficiency of engine is

= \frac{W}{Q_{1}}

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efficiency of engine is

= 1 - \frac{Q_{1}}{Q_{2}}

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Solution

The correct option is C efficiency of engine is $= \frac{W}{Q_{1}}$
The second law of thermodynamics states , that it is impossible to construct a heat engine , operating in cycle , which extracts heat and can convert it all to useful work .In other words , it is impossible for a heat engine to convert heat completely in work .
The efficiency of a heat engine is the ratio of net work done per cycle by engine to the heat absorbed per cycle by engine from reservoir ,
$η = \frac{W}{q_{1}} = \frac{Q_{1} - Q_{2}}{Q_{1}} = 1 - \frac{Q_{2}}{Q_{1}}$
if $Q_{2} = 0$ i.e. heat is not given to sink , it means total heat absorbed is converted into work , then
$η = 1$ , which is practically not possible .
Therefore $Q_{2} \neq 0$ .
Now as $Q_{1} - Q_{2} = W$ , therefore $Q_{2} > W$ .

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