Question

A Black metal foil receives radiation of power
P from a hot sphere at absolute temperature
1, kept at a distance d. If the temperature is
doubled and distance is halved, then Power
will be
1) 64P 2) 16P 3) 4P 4) 8P
7
TO



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Answer 1

Answer:

the answer is 1)64 p any doubts

Answer 2

Answer:

The power will be four times of the power at absolute temperature.

Explanation:

We know,

Power is directly proportional to fourth power of temperature.

    $P$  ∝  $(T^{4}-T^{4}_{o})$

T₀ is absolute temperature and   T₀<<<T

∴    P  ∝ $T^{4}$                                                       ................(1)

Now d is the between the hot sphere and black metal foil.

Energy received will be:  P  ∝  $\frac{1}{d^{2}}$                     ................(2)

By combining eq. (1) and (2)

       P  ∝   $\frac{T^{4}}{d^{2}}$

Now $T_{1}=T,T_{2}=2T$ and  $d_{1}=d, d_{2}=2d$

           $\frac{P_{1}}{P_{2}} =(\frac{T}{2T})^{4} *(\frac{2d}{d})^{2}$

∴          $\frac{P_{1}}{P_{2}}=\frac{1}{4} \\ P_{2}=4P_{1}$

Therefore   $P'=4P$

Therefore the option (3) is correct.