Question

what will be effect on beats of earth if temperature of sun is increased 4 times

Answer 1

Answer:

The power radiated per unit area is increased by a factor of 256.

Explanation:

According to the Stefan-Boltzmann law, the power radiated from a surface is proportional to the fourth power of its temperature.

Mathematically, it is represented as follows:

P/A = eσT⁴, where P/A is the power radiated per unit area, e is the emissivity, σ is the Stefan's constant, and T is the temperature.

If the temperature is increased, the power radiated will also increase. However, the area A and emissivity e will remain the same.

Let P₁, P₂ be the power radiated and T₁, T₂ be the temperatures. It is given that T₂ = 4T₁.

$\frac{\frac{P_1}{A}}{\frac{P_2}{A}} = \frac{eT_1^4}{eT_2^4}$

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

$\frac{P_1}{P_2} = (\frac{T_1}{T_2})^4$

$\frac{P_1}{P_2} = (\frac{T_1}{4T_1})}^4$

$\frac{P_1}{P_2} = (\frac{1}{4})^4$

$\frac{P_1}{P_2} = \frac{1}{256}$

P₂ = 256P₁

Therefore, if the temperature of the Sun is increased 4 times, the power radiated is increased 256 times.

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Answer 2

$T^{4} _{2}$Answer:

when the  effect on beats of earth if temperature of sun is increased 4 times it will be 256 times.

Explanation:

To understand about the sun temperature when it is increased due to temperature, we follow the laws related to Stefan-Boltzmann:

According to the law of Stefan-Boltzmann, "it explains that when the power of the radiation from the surface will be directly proportional to the 4th power of the its own temperature."

The formula for this law is,

P/A = eσT

Here, P/ A is known as the power of the radiation in per unit area

E is known as the emissivity

σ  Is known as constant of the Stefan

T is known as the temperature

• It can proved that, when the temperature is increased, the power will be radiated and it will increase it.
• The area called A and the emissivity called e is remained the same.

Proving by a theory calculation :

Let us consider that, P1 and P2 are the power of radiation and T1 and T2 are the temperatures.

Hence, the value of T2 = 4T1.

Now, we are going to divide each of them, We get,

P1/A/P2/A = e $T^{4} _{1}$/ e $T^{4} _{2}$

When we cancel A and e we get,

P1/P2 = $T^{4} _{1}/ T^{4} _{2}$

P1/p2 = t1/t2  to power of 4

P1/p2 = t1/4t1 power of 4

P1/p2 – ¼ to the power of 4

P1/p2 = 1/256

Therefore, P2 = 256 p1

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