GATE 2026 AE – Question 53
A furnace of 250 MW rating is used to melt and raise the temperature of aluminium from 25 $^o$C to 900 $^o$C. Aluminium has a solid-state specific heat, latent heat, and liquid-state specific heat of 0.9 kJ/kg-K, 390 kJ/kg, and 1.108 kJ/kg-K, respectively, and the furnace has 70% efficiency. The melting point of aluminium is 660 $^o$C. The amount of aluminium that can be processed per hour is ________ kg (rounded off to 1 decimal place).
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Correct answer: 510705.34 to 515838.06
Explanation
The heat needed per kg is $0.9(660 - 25) + 390 + 1.108(900 - 660) = 571.5 + 390 + 265.92 = 1227.42$ kJ/kg. The useful power is $0.7 \times 250000 = 175000$ kW, or $175000 \times 3600 = 6.3 \times 10^8$ kJ per hour. The mass per hour is $\frac{6.3 \times 10^8}{1227.42} = 513271.7$ kg.