Consider a Carnot’s cycle operating between T1 = 500K and T2 = 300K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.
Consider a Carnot’s cycle operating between T1 = 500K and T2 = 300K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

Answer:

According to the question, the temperature of the source is T1 = 500 K and the temperature of the sink is T2 = 300 K

We also have the work done per cycle as W = 1 kJ = 1000 J

we have to determine the heat transferred to the engine per cycle, Q1 =?

The expression for the efficiency of a Carnot engine si as follows:

\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}=1-\frac{300}{500}

\eta =\frac{2}{5}

\eta =\frac{W}{{{Q}_{1}}}\Rightarrow {{Q}_{1}}=\frac{W}{\eta }

{{Q}_{1}}=2500J

{{Q}_{1}}-{{Q}_{2}}=W

{{Q}_{2}}={{Q}_{1}}-W=2500-1000

{{Q}_{2}}=1500J