An insulated compressor uses 25 hp of power to compress air from 14.7 psia to 80 psia. The air enters at 75oF, and the volumetric flow rate at the inlet is 2.50 ft3/s. Determine the temperature of the air exiting the compressor.
Given: P1 = 14.7 psia; T1 = 75oF; P2 = 80 psia; W?= ?25 hp=?17.67 Btu/s; V?= 2.50 ft3/s; Air (Take State 1 as the inlet, State 2 as the outlet.)
Assume: Q?=0 (insulated). 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 W?=m?(h1?h2)
Here, not knowing the final temperature, we will consider the air to have variable specific heats, and then use the exit enthalpy to find the exit temperature from on-line properties or tables.
We also need to find the mass flow rate:
v1 = RT1/P1 = (53.33 ft-lbf/lbm-R) (75+460)R/ (14.7)(lbf/in2)(144 in2/ft2) = 13.48 ft3/lbm
m?=V1?/v1 =0.185 lbm/s
For T1: h1 = 127.86 Btu/lbm
h2=h1?W?m? =223.4 Btu/lbm
This corresponds to a temperature of T2 = 929 R = 469°F .
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