Question

A reciprocating air compressor takes in 2m/min air at 0.11m/min air at 0.11 MPa, 20°C, and delivers it at 1.5MPa, 111°C to an after cooler where, the air is cooled at constant pressure to 25°C. The power absorbed by the compressor is 4.15KW. Determine (1) The heat transfer in the compressor and cooler State your assumptions. Take C, of air is 1.005kg​

Answer 1

Answer: For comprosser: 8.137 Kg/sec

For cooler: -3.768 Kg/sec

Explanation:

Given,

V1= 2m³/min = 1/30 m³/sec

P1= 0.11 MPa = 0.11 × 10⁶ N/m²

T1= 20°C

P2= 1.5×10⁶ N/m²

T2= 111°C

T3= -28°C

W= 4.15 KW

Cp= 1.005 KJ/KgK

From SFEE,

Q - Ws = mf[h₂⁻h₁] +1/2 [V₂²-V₁²] +g[Z₂-Z₁]

Since elevation and velocity is not given,

Q₁₋₂ - W₁₋₂ = m[ Cp( T₂- T₁)....(i)

now,

P₁V₁ = mRT₁

m = (0.11x10⁶x1/30) / (287x293)   [R of air = 287]

now from equation (i) for compressor,

Q₁₋₂ - 4.15= 0.0436[1.005X10⁵(111-20)]

Q₁₋₂= 8.137 KJ/sec

and for cooler,

Q₂₋₃ - 0= 0.0436[1.005x10³(-111+25)]

Q₂₋₃= -3.768 KJ/sec