Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Radiated Power from Blackbody

黑体辐射的功率
When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant.
Calculation
计算

The total power radiated by a blackbody is given by the Stefan-Boltzmann equation, but it is often interesting to know the fraction of power which is emitted in the visible or some other wavelength range.

黑体辐射的总功率由斯特藩-玻尔兹曼定律给出，但有时也有趣知道在可见光或其他波长范围内发射的功率占总功率的份额。

Temperature T = K = °C

温度 T = K = °C
中文译文中的待填/计算数值依次对应：1：th 2：thc。实际数值以上方原输入框为准。

Area A = cm2 = x10^ m2

面积 A = cm² = 10^x m²
中文译文中的待填/计算数值依次对应：1：racm 2：rab 3：rap。实际数值以上方原输入框为准。

Emissivity = (e = 1 for ideal radiator)

发射率 = (e = 1 对理想辐射体)
中文译文中的待填/计算数值依次对应：1：em。实际数值以上方原输入框为准。

The total power radiated is P = watts = x10^ watts.

总辐射功率是 P = 瓦特 = x10^ 瓦特。
中文译文中的待填/计算数值依次对应：1：qt 2：qtb 3：qtp。实际数值以上方原输入框为准。

Finding the power radiated within a given wavelength range requires integration of the Planck radiation formula over that range. The radiated power per unit area is the Planck energy density multiplied by c/4. It can be approximated numerically by taking a sum of values of the Planck radiation density times a wavelength interval. The result of dividing the wavelength interval into 100 steps is as follows.

在给定波长范围内求出辐射的功率，需要对Planck辐射公式在该范围内进行积分。单位面积辐射的功率等于Planck能量密度乘以c/4。它可以通过将Planck辐射密度值与波长区间相乘并求和来近似计算。将波长区间分成100步的结果如下。

For the wavelength range λ1 = nm to λ2 = nm,

对于波长范围从 λ₁ = nm 到 λ₂ = nm，
中文译文中的待填/计算数值依次对应：1：w1 2：w2。实际数值以上方原输入框为准。

The radiated power is Pinterval = watts = x10^ watts.

辐射功率是 P interval = 瓦特 = x10^ 瓦特。
中文译文中的待填/计算数值依次对应：1：qti 2：qtib 3：qtip。实际数值以上方原输入框为准。

This is % of the total radiated power.

这是总辐射功率的%。
中文译文中的待填/计算数值依次对应：1：per。实际数值以上方原输入框为准。

The radiated power in a given wavelength interval Δλ at wavelength λ can be approximated by

在波长λ的某个波长区间Δλ内辐射的功率可以近似表示为

The above approximate calculation for the radiated power in a chosen wavelength range is a brute force sum over 100 terms formed by dividing the specified wavelength range into 100 parts. This is then compared to the total radiated power calculated from the Stefan-Boltzmann equation. You can check out the calculation by choosing the wavelength range so that it covers essentially all the radiated energy. You will find that the calculation diverges if you pick a starting wavelength too close to zero, and if you put in too large a wavelength. But by examining the wavelength range for which the radiated power appears to be significant, you can choose reasonable limits on wavelength and confirm that you get essentially all the radiated power.

上述对选定波长范围内辐射功率的近似计算，是通过将指定波长范围分成100份，形成100项后进行的粗暴求和。然后将其与由斯特藩-玻尔兹曼方程计算出的总辐射功率进行比较。你可以通过选择一个覆盖几乎所有辐射能量的波长范围来验证该计算。如果你选择的起始波长太接近零，或者波长范围太大，计算结果会发散。但通过检查辐射功率显著的波长范围，你可以选择合理的波长限制，并确认你实际上获得了几乎所有辐射的功率。
当黑体辐射体的温度升高时，总的辐射能量增加，辐射曲线的峰值向更短的波长移动。当从普朗克辐射公式中求出最大值时，峰值波长与温度的乘积被发现是一个常数。
 Index

Blackbody radiation concepts
索引 黑体辐射概念
 
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