Question

An irreversible heat engine extracts heat from a high temperature source at a rate of $100kW$ and rejects heat to a sink at a rate of $50kW$. The entire work output of the heat engiine is used to drive a reversibel heat pump operating between as set of independent isothermal heat reservoirs at ${17}^{o}C$ and ${75}^{o}C$. The rate (in$kW$) at which the heat pump delivers heat to its hight temperature sink is

• A. $360$
• B. $250$
• C. $300$
• D. $50$

Answer 1

The correct option is C $300$

Given data:



Heat engine work output,
$W=Q_1-Q_2=100-50=50kW$
$=$Pump input work
$(COP{)}_{HP}=\frac{Q_4}{W}$
also $(COP{)}_H=\frac{T_4}{T_4-T_3}$
$\therefore \frac{Q_4}{W}=\frac{T_4}{T_4-T_3}$
$\frac{Q_4}{50}=\frac{348}{348-290}=\frac{348}{58}$
or $Q_4=300kW$