Question

A combination of a heat engine driving a heat pump (see Fig. P7.106) takes waste energy at 50°C as a source Qw1 to the heat engine rejecting heat at 30°C. The remainder Qw2 goes into the heat pump that delivers a QH at 150°C. If the total waste energy is 5 MW find the rate of energy delivered at the high temperature.

Answer 1

Answer:

1.08 MW

Explanation:

Given that:

Heat supplied to heat engine

$Q_{WS}$ = 5 MW

Temperature of the hot source of engine

$T_{WS}$ = 323 K

Temperature of the cold source of engine

$T_L$ = 303 K

the temperature and heat relation for a reversible heat engine can be presented as follows:

$\frac{T_L}{T_{WS}} =\frac{Q_L}{Q_{WS}}$

$\frac{303}{323} =\frac{Q_L}{5}$

$Q_L$ = 4.69 MW

TO determine the work done by the heat engine ; we have:

$W_{engine}=Q_{WS}-Q_{L}$

$W_{engine}=5 -4.69$

$W_{engine}=0.309MW$

The temperature and heat relation for the reversible heat pump can be written as:

$\frac{T_H}{T_L}=\frac{Q_H}{Q_L}$

$\frac{T_H}{T_L}=\frac{Q_H}{Q_H-W}$

$\frac{423}{303} =\frac{Q_H}{Q_H-W}$

$Q_H=1.396-0.309\\Q_H=1.08MW$