Question:
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.
Solution:
Given,
Temperature of the source, T1 = 500 K
Temperature of the sink, T2 = 300 K
Work done per cycle, W = 1 kJ = 1000 J
Heat transferred to the engine per cycle, Q1 =?
Efficiency of a Carnot engine
$\eta=1-\frac{T_{2}}{T_{2}}=1-\frac{300}{500}=\frac{2}{5}$
$\eta=\frac{W}{Q_{1}} \Rightarrow Q_{1}=\frac{W}{\eta}=2500 \mathrm{~J}$
$Q_{1}-Q_{2}=W, Q_{2}=Q_{1}-W$
= 2500 J – 1000 J = 1500 J