Please see attached image. Your help is greatly appreciated. A single stage vapo

Question

Please see attached image.  Your help is greatly appreciated.

A single stage vapor machine has a cooling duty of 20 kJ/s the refrigosant in 134 a Evaporating pressure is 4.0 bar (0 middot 4 Mpa) Condonsing pressue is 12.0 bar (1 middot 2 Mpa) Refrigecant enters the at 10 degree c (1.09 degree C superheat) enters the expansion value as a saturated liquid. Expansion is isentralpic Compressor efficiency in 05%. Determine The required R 134 a flow rate. The required compressor power The cooling COP also Draw the p-h-diagram.

Explanation / Answer

R-134a properties:

At P1 = 4 bar and T1 = 10 deg C, we get h1 = 257 kJ/kg, s1 = 0.931 kJ/kg-K

For isentropic compression, s2_is = s1 = 0.931 kJ/kg-K

At P2 = 12 bar and s2_is = 0.931 kJ/kg-K, we get h2_is = 280 kJ/kg

At P3 = P2 = 12 bar and quality = 0 (sat. liquid), we get h3 = 118 kJ/kg

During expansion in throttling, h4 = h3 = 118 kJ/kg

Compressor efficiency = (h2_is - h1) / (h2 - h1)

0.85 = (280 - 257) / (h2 - 257)

h2 = 284 kJ/kg

a)

Cooling duty = m*(h1 - h4)

20 = m*(257 - 118)

m = 0.144 kg/s

b)

Compressor power = m*(h2 - h1)

= 0.144*(284 - 257)

= 3.88 kW

c)

COP = Cooling duty / Compressor power

= 20 / 3.88

= 5.148

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