Question

A refrigerator operates on the reversed Carnot cycle and uses water as the working

fluid. At the beginning of the isothermal expansion, the steam has an absolute

pressure of 1kPa and a quality of 7%; at the end of the isothermal expansion, the

steam is dry and saturated. At the end of heat rejection process the water is saturated

liquid. Firstly: Sketch the T‐s and P‐v diagrams for the cycle, and secondly: for one kg

of water, calculate: a) The steam pressure at beginning of the heat rejection process,

b) the net work per cycle, c) the COP of the cycle in two conditions: 1‐refrigeration

and 2‐heat pump

Answer 1

The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP):

$COP_R = \frac{Q_L}{W_{in}}$

$COP_{HP} = \frac{Q_H}{W_{in}}$

Reversed Carnot Cycle:

An internally, reversible, constant pressure heat rejection

$Q_H = h_2 − h_3$ ...$h_3 =h4$

An internally, reversible, constant pressure heat interaction

$Q_L = h_1− h_4$