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Thermodynamics
First Law of Thermodynamics
GATE 2014
Medium

In a power plant, water (density = 1000 kg/m³) is pumped from 80 kPa to 3 MPa. The pump has an isentropic efficiency of 0.85. Assuming that the temperature of the water remains the same, the specific work (in kJ/kg) supplied to the pump is

  • A0.34
  • B2.48
  • C2.92
  • 3.43

Explanation

Specific volume v=1/ρ=0.001 m³/kg. Ideal (isentropic) pump work = v·Δp = 0.001×(3000−80) = 2.92 kJ/kg. Since a real pump requires MORE work than the ideal case, actual work = ideal/η = 2.92/0.85 ≈ 3.43 kJ/kg.

Source: GATE ME 2014 (Session 1 / Set-1) (2014)

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