Question

On tripling the absolute temperature of the source,the efficiency of carnot's heat engine becomes double that of the initial efficiency. Then the initial efficiency of the engine is

Answer 1

Answer:

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Answer 2

Answer:

The initial efficiency of the engine is $\frac{4}{7}$

Explanation:

Let the initial source temperature be $T_{1}$

Then, new source temperature $= 3T_{1}$

Let the initial efficiency be η

Then, new efficiency $=$ 2η

Our aim is to find the initial efficiency i.e. η

We can relate efficiency and temperature using the following formula:

η $= 1-(\frac{T_{2} }{T_{1} } )$

In the formula, η refers to efficiency, $T_{2}$ is sink temperature and $T_{1}$ is source temperature.

By considering the given values, using them in the equation :

2η= $= 1-(\frac{T_{2} }{3T_{1} } )$

Replacing η with formula :

$2[1-(\frac{T_{2} }{T_{1} } )] = 1-(\frac{T_{2} }{3T_{1} } )$

$2T_{1} -2\frac{T_{2} }{T_{1} } = 3T_{1} -\frac{T_{2} }{3T_{1} }$

$\frac{T_{2} }{T_{1} } = \frac{3}{7}$

Keeping  $\frac{T_{2} }{T_{1} }$ in the original equation :

η $=1-(\frac{3}{7} )$

η $=\frac{4}{7}$

Hence, Initial efficiency of engine is $\frac{4}{7}$.