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Allisa [31]
3 years ago
11

What temperature increase is necessary to increase the power radiated from an object by a factor of 8?

Physics
1 answer:
Aleks04 [339]3 years ago
7 0

To solve this problem it is necessary to apply the concepts related to the Power defined from the Stefan-Boltzmann equations.

The power can be determined as:

P = \sigma T^4

Making the relationship for two states we have to

\frac{P_1}{P_2} = \frac{T_1^4}{T_2^4}

Since the final power is 8 times the initial power then

P_2 = 8P_1

Substituting,

\frac{1}{8} = \frac{T_1^4}{T_2^4}

T_2 = T_1 8*(\frac{1}{4})

T_2 = 1,68T_1

The temperature increase would then be subject to

\Delta T = T_2-T_1

\Delta T = 1.68T_1 -T_1

\Delta T = 0.68T_1

The correct option is D, about 68%

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