A metal ball of radius 0.1 m at a uniform temperature of 90°C is left in air at 30°C. The density and the specific heat of the metal are 3000 kg/m3 and 0.4 kJ/kg.K respectively. The heat transfer co-efficient is 50 W/m2.K Neglecting the temperature gradients inside the ball, the time taken (in hours) for the ball to cool to 60°C is_________________?
Correct answer: D. 0.15
- A. 555
- B. 55.5
- C. 0.55
- D. 0.15
Explanation
For a lumped sphere, the time constant is ρc_pr/(3h) = 800 s. Since (60−30)/(90−30) = 0.5, t = 800 ln 2 = 554 s ≈ 0.15 h, so the very large values are in seconds, not hours.
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