Question

7. We decide to store 200 MJ of electrical energy by driving a heat pump which transfers heat from 20°C to molten salt at 500°C. This energy is retrieved later by running a heat engine between the same two temperatures. Both the heat pump and the engine can be described by efficiencies WIQH, and they both have the same ideal (Carnot) efficiency. A. What is the ideal efficiency of the heat pump? B. molten salt? Assuming ideal efficiency, how much heat energy is transferred to the The actual efficiency of the engine is only 50%. How much work is C. retrieved?

Answer 1

(A) Ideal efficiency of the heat pump,

The ideal efficiency is the carnot efficiency and it is given by ,

n=1- TL TH = 1 (273 + 20 (273+500)

$\eta =0.621$ = 62.1 %

(B)Using the ideal efficiency , heat supplied to molten salt is given by ,

$\eta =\frac{W_{in}}{Q_{H}}$

$0.621 =\frac{200}{Q_{H}}$

ен 322MJ

(C) The work output for 50% efficiency is,

$\eta =\frac{W_{in}}{Q_{H}}$

$0.5 =\frac{W_{in}}{322}$