# Consider a Carnot’s cycle operating between

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
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