When a completely black body cools down, its maximum

As the black body cooled, its spectral maximum emission shifted by 500 nm. To determine how many degrees a body has cooled, you need to use Wien's law. From this law it follows that the spectral maximum of an absolutely black body is proportional to its temperature. Thus, we can create an equation:

λ_max2 / λ_max1 = T1 / T2,

where λ_max1 and λ_max2 are the spectral maxima of the body at the initial and final temperatures T1 and T2, respectively.

Solving this equation for T2, we get:

T2 = T1 / (λ_max2 / λ_max1).

Substituting the values ​​λ_max1 = 500 nm and T1 = 2000 K, we obtain:

T2 = 2000 / (500 + 500) = 2000 / 1000 = 2 K.

Thus, the body cooled by 1998 degrees (initial temperature 2000 K minus final temperature 2 K).

Cargo code: 50183

Product name: Solution to the problem “When an absolutely black body cools, the maximum of its emission spectrum”

Product description: By purchasing this digital product, you will receive a complete and detailed solution to the problem associated with cooling an absolutely black body and shifting the maximum of its emission spectrum by 500 nm. In the solution file you will find a summary of the conditions, formulas and laws used in the solution, as well as the output of the calculation formula and the final answer. If you have any questions about the solution, our team is ready to help you.

Price: 99 rubles

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Solution to the problem “When a black body cools, the maximum of its emission spectrum”

Cargo code: 50183

Price: 99 rubles

By purchasing this digital product, you will receive a complete and detailed solution to the problem associated with cooling a black body and shifting the maximum of its emission spectrum by 500 nm. In the solution file you will find a summary of the conditions, formulas and laws used in the solution, as well as the output of the calculation formula and the final answer. If you have any questions about the solution, our team is ready to help you.

This product is a brief and detailed solution to problem No. 50183, associated with cooling a black body and shifting the maximum of its emission spectrum by 500 nm. In the solution file you will find a record of the conditions, the formulas and laws used, as well as the output of the calculation formula and the answer to the question posed. The task is to determine how many degrees the body has cooled at an initial temperature of 2000 K and to shift the maximum of its emission spectrum by 500 nm. The solution is based on Wien's law and leads to the answer that the body has cooled by 1998 degrees. The cost of this digital product is 99 rubles. If the buyer has questions about the solution, the seller's team is ready to help.

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This product is a problem from the field of thermodynamics and optics.

Condition of the problem: when a black body cools, the maximum of its emission spectrum shifts by 500 nm. It is necessary to find how many degrees the body cooled if the initial temperature was 2000 K.

To solve the problem, Wien's displacement law is used, which establishes the dependence of the maximum of the radiation spectrum of an absolutely black body on its temperature. The formula of the law has the form: λ_maxT = b, where λ_max is the wavelength of the spectrum maximum, T is the absolute body temperature, b is a constant equal to 2898 μm*K.

Using this formula, we find the initial wavelength of the maximum of the black body radiation spectrum at the initial temperature T1 = 2000 K: λ_max1 = b/T1.

Further, according to the conditions of the problem, when the body cooled, the wavelength of the maximum of the radiation spectrum shifted by 500 nm, which is equal to 0.5 μm. Thus, the wavelength of the spectrum maximum when the body cools is λ_max2 = λ_max1 + 0.5 μm.

Using the formula of Wien's displacement law for the second temperature T2, we find the desired temperature: T2 = b/λ_max2.

So, the calculation formula for finding the body temperature when cooling is: T2 = b/(λ_max1 + 0.5 μm).

Substituting the values ​​of the constant b and the initial temperature T1, we obtain: T2 = 2898/((1.44910^-3) + 0.510^-6) ≈ 1669 K.

Answer: the body cooled by (2000 - 1669) ≈ 331 degrees on the Kelvin scale.

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