First slide

Heat transfer-Radiation

Question

A metal cylinder of 5 kg is heated electrically by a 20 W heater in a room 20^oC. The cylinder temperature rises uniformly to 30^oC in 5 minute and finally becomes constant at 45^oC. Assuming that the rate of heat loss is proportional to the excess temperature over the surroundings.

Moderate

A

the rate of loss of heat of cylinder to surrounding at 25^oC is 4 W
B

the rate of loss of heat of cylinder to surrounding at 45^oC is 20 W
C

the rate of loss of heat of cylinder to surrounding at 25^oC is 8 W
D

the rate of loss of heat of cylinder to surrounding at 45^oC is zero

Solution

$\begin{array}{l} T_{room} = 20^{\circ} C \\ m_{cylinder} = 5 kg \\ P = 20 W \end{array}$
Since temperature becomes constant at 45°C
$\Rightarrow$ Power lost at 45°C = 20 W
From Newton's law of cooling
$\begin{array}{l} ∴ {|\frac{d Q}{dt}|}_{T = 45^{\circ} C} = 20 = K (45 - 20) \\ \Rightarrow K = \frac{4}{5} \end{array}$
Since temperature rises uniformly to 30°C thus, at 25°C,
$\frac{d Q}{dt} = k (25 - 20) = 4 W$

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