Question

Для определения эффективной температуры звёзд используют закон Стефана — Больцмана, согласно которому мощность излучения нагретого тела Р прямо пропорциональна площади его поверхности S и четвёртой степени температы: P=σST4, где σ=5,7⋅10−8 - постоянная, площадь измеряется в квадратных метрах, температура — в градусах Кельвина, а мощность — в ваттах. Известно, что некоторая звезда имеет площадь S=1/18*10^21 а излучаемая ею мощность P не менее 4,104*10^27. Определить наимешаю возможную температуру этой звезды. Ответ дать в градусах Кельвина

Answer 1

$4.104*10^{27} = 5.7*10^{-8}*\frac{1}{18}*10^{21}*4*T </p> <p>T= \frac{4.104*10^{27}}{5.7*10^{-8}*\frac{1}{18}*10^{21}*4}</p> <p>T= 324*10^{12}$

Answer 2

To determine the effective temperature of a star using the Stefan-Boltzmann law, we can use the equation P = σST^4, where P is the power of radiation emitted by the star, S is the surface area of the star, T is the temperature of the star in Kelvin, and σ is the Stefan-Boltzmann constant, which is approximately 5.7 x 10^-8 W/(m^2·K^4).

In this case, we are given that the surface area of the star is S = (1/18) * 10^21 m^2 and the power emitted by the star is P ≥ 4.104 * 10^27 W. We need to determine the minimum possible temperature of the star.

To find the minimum temperature, we can rearrange the equation to solve for T:

T^4 = P / (σS)

Taking the fourth root of both sides, we get:

T = (P / (σS))^(1/4)

Substituting the given values, we have:

T = (4.104 * 10^27 W) / (5.7 x 10^-8 W/(m^2·K^4) * (1/18) * 10^21 m^2)^(1/4)

Simplifying the expression inside the parentheses:

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