Oil, with a density of 910 kg/m3 and a specific heat of 1.8 kJ/kg-K is in an pump. The pump increases the pressure of the oil from 100 kPa to 5000 kPa, while the oil temperature increases from 40°C to 90°C. Determine the changes in specific internal energy and specific enthalpy of the oil. At what final pressure, would you consider it acceptable to disregard the pressure component of the specific enthalpy change?

Question

Given: p = 910 kg/m3; c = 1.8 kJ/kg-K; P1 = 100 kPa; P2 = 5000 kPa; T1 = 40°C; T2 = 90°C

What will be an ideal response?

Answer 1

v = 1/p = 0.001099 m3/kg
Assuming the oil to behave as an incompressible substance with constant specific heats:
?u = c (T2 – T1) = 75 kJ/kg
?h = c (T2 – T1) + v (P2 – P1) = 80.4 kJ/kg
The pressure term adds 7% to the value, which is somewhat large. If one were to consider 5% as acceptable to ignore, then the pressure change should be no more than
3.75 kJ/kg:
3.75 kJ/kg = v (P2 – P1)
P2 = 3510 kPa