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A small copper ball of 5 mm diameter at 500 K is dropped into an oil bath whose temperature is 300 K. The thermal conductivity of copper is 400 W/mK, its density 9000 kg/m3 and its specific heat 385 J/kgK. If the heat transfer coefficient is 250 W/m2K and lumped analysis is assumed to be valid, the rate of fall of the temperature of the ball at the beginning of cooling will be, in K/s,
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- 8.7
- 13.9
- 17.3
- 27.7
Correct Option: C
Given data: K = 400 W/mK; Ti = 500 K ; ρ = 9000 Kg/m3.
T∞ = 300 K; Cp = 385 J/KG K; h = 250 W /m2K
| Lc = | = | = | = 8.33 × 10-4 | |||
| A | 6 | 6 |
| T = T∞ + (Ti - T∞) e | ||
| ρcV |
| = | (Ti - T∞) e | ||||
| dt | ρcV | ρcV |
 |  | = | (Ti - T∞) | ||||
| dt | t = 0 | ρcV |
| = | = 17.31 K / S | |
| 9000 × 385 × 8.33 × 10-4 |
