GATE 2026 ME – Question 56
A liquid comes out of the reactor of a chemical plant at 250 °C temperature with a flow rate of 100 LPM. The ambient temperature is 25 °C. Density and specific heat of the liquid remain constant at 1000 kg/m$^3$ and 4.18 kJ/kg K, respectively, for the given range of temperature. The rate of exergy associated with the hot liquid stream at the exit of the plant is ________ kW (*rounded off to 2 decimal places*).
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Correct answer: 397.59 to 401.59
Explanation
The mass flow rate is $100\ \text{L/min} = 100$ kg/min $= 1.667$ kg/s. The specific exergy of the stream relative to the ambient is $c\left[(T - T_0) - T_0\ln\frac{T}{T_0}\right]$ with $T = 523.15$ K and $T_0 = 298.15$ K. That is $4.18\left[225 - 298.15\ln(1.7547)\right] = 4.18 \times 57.36 = 239.75$ kJ/kg. The exergy rate is $1.667 \times 239.75 = 399.59$ kW. The last digits depend on whether 273 or 273.15 is used for the Kelvin conversion.