A black body at 227^° C radiates heat at the rate of 7 cals / cm^2 ~s . At a temperature of 727^° C , the rate of heat radiated in the same units will be :

Correct answer: (D) 112. P ∝ T^4 P_2/P_1= (1000/500 )^4 P_2=16 P_1=112

Q109 / 197 · NEET 2009 (Mains) · Physics

A black body at $227^{\circ} \mathrm{C}$ radiates heat at the rate of $7 \mathrm{cals} / \mathrm{cm}^2 \mathrm{~s}$. At a temperature of $727^{\circ} \mathrm{C}$, the rate of heat radiated in the same units will be :

A
80
B
60
C
50
Correct answer
D
112

Solution

$\mathrm{P} \propto \mathrm{T}^4$ $$ \begin{aligned} & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{1000}{500}\right)^4 \\ & \mathrm{P}_2=16 \mathrm{P}_1=112 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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