Question

A standard vapour compression refrigeration cycle operating with a condensing tenperature of ${35}^{\circ }C$ and an evaporating temperature of $-{10}^{\circ }C$ develops $15kW$ of cooling). The P-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is $0.75$, the magnitude of compressor power (in kW) is (correct to two decimal places)

Answer 1

$RC=15kW$

$RC=m\times (h_1-h_4)$

$=15=m\times (400-250)$

$m=0.1kg/s$

\(η _{isentropic} = (h_2-h_1) = (475-400)\)
$=75kJ/kg$

\(eta_C= \dfrac{η _{isentropic}}{η _{actual}}\)

\(η _{actual} = \dfrac{75}{0.75} = 100~kJ/kg\)

\(P_{in} = m \times η _{actual} = 0.1 \times 100\)

$P_{in}=10kW$