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A metal sphere cools at the rate of 4°C/min. when its temperature is 50°C. Find its rate of cooling at 45°C if the temperature of surroundings is 25°C. |
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Answer» Given: θ0 = 25ºC, θ1 = 50ºC, θ2 = 45ºC, [\(\frac{d\theta}{dt}\)]1 = 4ºC/,om To find: Rate of cooling at θ2 (\(\frac{d\theta}{dt}\))2 Formula: \(\frac{d\theta}{dt}\) = K (θ-θ0) Calculation: Using formula, for θ1 = 50ºC 4 = K (50-25) ∴ K = \(\frac{4}{25}\) min-1 ∴ θ2 = 45ºC (\(\frac{d\theta}{dt}\))2 = \(\frac{4}{25}\) x (45-25) = \(\frac{4}{25}\) x (20) = \(\frac{16}{5}\) = 3.2ºC/min The rate of cooling at 45 ºC is 3.2ºC/min. |
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