Question 4
A heat pump operates irreversibly to extract heat from the atmosphere at a temperature of
7-\deg C
and deliver
43,200k(J)/(h)r
of heat to a constant-temperature reservoir at 420 K . The efficiency of this heat pump is
80%
of the efficiency of a Carnot heat pump operating between the same temperature limits. The heat pump is powered by a heat engine that draws heat from a constant-temperature reservoir at 1000 K and rejects waste heat to a separate reservoir at
400-K
, which is the same reservoir used by the heat pump. The thermal efficiency of the engine is
75%
of the efficiency of a Carnot heat engine operating between the same temperature limits. Additionally, the transmission that transfers the actual work output of the heat engine to the heat pump has an efficiency of only
80%
. Determine:
4.1. The power input required for the actual heat pump in kW
(8)
4.2. The rate of heat input from the 1050 K reservoir to the actual engine in
k(J)/(h)r
4.3. The percentage of the total heat supplied to the
420-K
reservoir that is delivered by the heat pump.
(3)
[15 Marks]
TOTAL MARKS [55]
UNISA 2025