An uninsulated compressor receives 0.5 m3/s of saturated water vapor at 100 kPa through a duct with a cross-sectional area of 0.005 m2. Superheated steam exits at 800 kPa and 350°C, at a velocity of 15 m/s. The compressor uses 175 kW of power. Determine the rate of heat loss from the compressor.
Given: P1 = 100 kPa; x1 =1.0 (saturated vapor); A1 = 0.005 m2; P2 = 800 kPa; T2 = 350°C; W?= ?175 kW; V1?= 0.5 m3/s; Water (Take State 1 as the inlet, State 2 as the outlet.)
Assume: For a compressor, assume steady-state, steady-flow, single-inlet, single-outlet flow, with ?KE = ?PE = 0
With these assumptions, the First Law for open systems reduces to Q?=m?(h2?h1)+W?
The known steam properties are
v1 = 1.694 m3/kg
h1 = 2674.95 kJ/kg
h2 = 3162.15 kJ/kg
The mass flow rate can be found from the inlet volumetric flow rate:
m?=V1?/v1 = 0.295 kg/s
Solving: Q?= -31.3 kW
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