Project ForgeA standard vapor compression refrigeration cycle operating with a condensing temperature of 35°C and an evaporating temperature of −10°C develops 15 kW of cooling. From the cycle's p-h diagram: h1 (evaporator exit, saturated vapor) = 400 kJ/kg, h2s (isentropic compressor exit) = 475 kJ/kg, h3=h4 (condenser exit / after throttling) = 250 kJ/kg. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is __________ (correct to two decimal places).
Explanation
Refrigeration effect per unit mass = h1−h4 = 400−250 = 150 kJ/kg. Mass flow rate ṁ = 15/150 = 0.1 kg/s. Isentropic compressor work per unit mass = h2s−h1 = 475−400 = 75 kJ/kg. Actual work per unit mass = 75/0.75 = 100 kJ/kg (isentropic efficiency reduces the useful cooling-to-work ratio, so actual work exceeds isentropic work). Compressor power = ṁ×w_actual = 0.1×100 = 10 kW.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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