GATE 2021 ME (ME2) – Question 60

Thermodynamics · Entropy changes, closed and open systems · 2 marks · Numerical answer

An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K. Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is _____ kW/K (round off to one decimal place).

Adiabatic vortex tube with high-pressure inlet 1, hot low-pressure outlet 2 and cold low-pressure outlet 3. See the attached source image.

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Correct answer: 2.19 to 2.21

Explanation

For ideal gas, $s_j-s_1=c_p\ln(T_j/T_1)-R\ln(p_j/p_1)$. With no heat transfer, entropy generation is the mass-weighted sum of those outlet-minus-inlet changes.

$\dot S_{gen}=3[1005\ln(340/300)-287\ln0.2]+2[1005\ln(240/300)-287\ln0.2]=2238.39$ W/K. **Answer: 2.2 kW/K**; the positive sign is consistent with irreversibility.