GATE 2025 CH – Question 50
An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg °C). Assuming water is incompressible with a density of 1000 kg/m$^3$, the maximum temperature rise of water across the pump is ____ °C (rounded off to 3 decimal places).
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Correct answer: 0.133 to 0.153
Explanation
The ideal (reversible) work per kg is $\frac{\Delta P}{\rho} = \frac{400 \times 10^3}{1000} = 400$ J/kg. The actual work with 40 % efficiency is $\frac{400}{0.4} = 1000$ J/kg. The first law for the adiabatic pump gives the enthalpy rise as 1000 J/kg, and for an incompressible fluid $\Delta H = c\Delta T + \frac{\Delta P}{\rho}$. So $c\Delta T = 1000 - 400 = 600$ J/kg and $\Delta T = \frac{600}{4200} = 0.143$ °C. This is the maximum, as no heat leaves the water.