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GATE 2019 ME (ME1) – Question 43

Thermodynamics · Zeroth, first and second laws, work, heat and energy changes · 2 marks · Multiple choice

Gas flows over a resistance heater supplied with 101 kW electrical power. It enters the duct at 100 kPa, 27°C and 15 m³/s; 51 kW is lost to surroundings. Assume constant pressure, ideal gas, negligible kinetic/potential changes and cp = 1 kJ/(kg·K), R = 0.5 kJ/(kg·K). Find exit temperature.

  1. 32°C
  2. 37°C
  3. 53°C
  4. 76°C

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Correct answer: (A) 32°C

Explanation

Inlet density is $\rho=p/(RT)=100/(0.5\cdot300)=2/3$ kg/m³, giving $\dot m=10$ kg/s. Net heating is $101-51=50$ kW. Then $\Delta T=50/(10\cdot1)=5$ K, so the outlet is **32°C, A**.