Consider a Carnot's cycle operating between `T_1` = 500 K and `T_2` = 300 K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

Explanation

Temperature of source `T_1` = 500 K
Temperature of sink `T_2` = 300 K
Work done per cycle W = 1 kJ = 1000 J
Heat transferred to the engine per cycle `Q_1` = ?
Efficiency of a carnot engine ,
`eta=1-T_2/T_1`
`=1-300/500`
`=200/500`
`=2/5`
Now, `eta=W/Q_1`
`therefore Q_1=W/ eta=1000/2xx5` = 2500 J
As `Q_1-Q_2=W`
`therefore Q_2=Q_1-W`=2500 J -1000 J = 1500 J