Question

A heat engine is operating between $500K$ to $400K$. If the engine absorbs $100J$ heat, then which of the following is an impossible amount of heat rejected by the engine?
(A) $80J$
(B) $85J$
(C) $90J$
(D) $10J$

Answer 1

Hint: We know that heat engine is an engine which converts the thermal energy into mechanical energy in thermodynamics. It is operated between a sink temperature and a source temperature. The source is at a higher temperature and the sink is at lower temperature.

Complete step-by-step answer:
As we know that heat engine converts the heat energy to mechanical energy. An ideal reversible heat engine is known as the Carnot engine. It is a theoretical engine. Efficiency is the ratio of useful work to that heat provided. An engine with more efficiency is preferable. Efficiency of a heat engine can be given as $\eta = 1 - \dfrac{{{T_2}}}{{{T_1}}} = 1 - \dfrac{{{Q_2}}}{{{Q_1}}} = \dfrac{{work\, done}}{{Heatgiven}}$. Here ${T_2} = $sink temperature, ${T_1} = $ source temperature, ${Q_2} = $ heat rejected ,${Q_1} = $ heat absorbed by the engine. In the question the value of ${T_1} = 500K,{T_2} = 400K,{Q_1} = 100J$ is given .
Now efficiency can be written as
$
   \Rightarrow \eta = 1 - \dfrac{{{T_2}}}{{{T_1}}} = 1 - \dfrac{{{Q_2}}}{{{Q_1}}} \\
   \Rightarrow 1 - \dfrac{{400}}{{500}} = 1 - \dfrac{{{Q_2}}}{{100}} \\
   \Rightarrow {Q_2} = \dfrac{{400}}{5} = 80J \\
 $

So from the above explanation and calculation it is clear to us that the correct answer of the given question is option: (A) $80J$.

Additional information: It is nearly impossible to design and create a heat engine that will have $100\% $ efficiency. Some examples of heat engines are thermal power stations, internal combustion engines and steam locomotives.

Note: Always remember that the efficiency of a heat engine can be given as $\eta = 1 - \dfrac{{{T_2}}}{{{T_1}}} = 1 - \dfrac{{{Q_2}}}{{{Q_1}}} = \dfrac{{work\, done}}{{Heatgiven}}$ , Here ${T_2} = $sink temperature, ${T_1} = $ source temperature, ${Q_2} = $ heat rejected ,${Q_1} = $ heat absorbed by the engine. Always avoid silly mistakes and calculation errors while solving the numerical.