Question

the power received at a distance d from a small metallic sphere of radius r and at temperature t isP If temperature is doubled and distance is reduced to half then power received at that point

Answer 1

Answer:

64 times the initial power.

Explanation:

According to inverse square law,

Power received  at a point (P) is inversely proportional to the distance of the power source.

P ∝ 1/D^2

Also,

Power received is directly proportional to the fourth power of the temperature.

P ∝ T1^4

So, combining the two, we get,

P ∝ T^4 / D^ 2

It is given that the temperature T is doubled. So, t = 2T

Also, the distance is reduced to half. So, d = 2D

Let 'p' be the power received at distance 'd' and temperature 't'.

Therefore,

P/p = T^4/D^2 / t^4/d^2

= (T/2T)^4  * (D/2/D)^2

=  1/16 * 1/4

P/p = 1/64

p = 64 P

Therefore, power received at the given point is 64 times the original power, when distance is reduced to half and temperature is doubled.

Answer 2

ans is 64p okkkkkkkkkkkkkkkkkkk