# How does a black body emit as much energy as it absorbs?

• GM Jackson
In summary, the conversation discusses the concept of a black body and how it absorbs all incident electromagnetic radiation, including visible light. It is noted that visible light has a higher frequency and energy compared to IR radiation, which leads to the question of how a black body achieves equilibrium when it absorbs visible light and emits IR. The conversation then delves into the relevant equations and the concept of energy balance before discussing the potential increase in temperature of the black body if it absorbs more energy than it radiates.

## Homework Statement

A black body absorbs all incident electromagnetic radiation, including visible light which has wavelengths from 380nm to 750nm. IR radiation has wavelengths that are so long they are measured in microns. That suggests that visible light has a higher frequency than IR, and, higher energy. So when a black body absorbs visible light and emits IR, how does it achieve equilibrium?

## Homework Equations

Ein = Eout (Energy in = Energy out)
E = hv (E = Energy; h = 6.63E-34 J-s; v = frequency in hertz)
v = C/l (C = 3.00E8 m/s; l = wavelength in meters)

## The Attempt at a Solution

I'm picturing in my mind the same amount of photons going in as going out, but this would imply more energy going in than going out. So what's up with the black body?

GM Jackson said:

## The Attempt at a Solution

I'm picturing in my mind the same amount of photons going in as going out, ..?

That's the problem. Far more low-energy photons are emitted, so the total in and out energy balance.

GM Jackson
GM Jackson said:
I'm picturing in my mind the same amount of photons going in as going out, but this would imply more energy going in than going out. So what's up with the black body?
Regardless of the number of photons involved, suppose the black body is absorbing more energy than it's radiating. It's not in equilibrium with its surroundings. What happens to the temperature of the black body?

GM Jackson
marcus said:
That's the problem. Far more low-energy photons are emitted, so the total in and out energy balance.
Thanks.

vela said:
Regardless of the number of photons involved, suppose the black body is absorbing more energy than it's radiating. It's not in equilibrium with its surroundings. What happens to the temperature of the black body?
I heard it goes up. Thanks for the input.

The way the question is worded implies that the blackbody isn't in equilibrium with its surroundings initially (otherwise it wouldn't have to do anything to achieve equilibrium), so it's not safe to assume the number of IR photons emitted is enough to maintain the energy balance. If you haven't already, you should consider what happens when the temperature of the blackbody goes up.

GM Jackson

## 1. What is a black body?

A black body is an idealized object that absorbs all radiation that falls on it and emits thermal radiation at all wavelengths. It is a theoretical concept used to explain the behavior of objects that absorb and emit radiation, such as stars and planets.

## 2. How does a black body emit energy?

A black body emits energy through thermal radiation, which is the emission of electromagnetic radiation due to the temperature of the object. As the black body absorbs energy, its temperature increases, causing it to emit thermal radiation at all wavelengths.

## 3. Why does a black body emit as much energy as it absorbs?

This is known as the principle of detailed balancing, which states that for a system in thermal equilibrium, the rate of absorption of energy must be equal to the rate of emission of energy. In other words, a black body emits as much energy as it absorbs in order to maintain a constant temperature.

## 4. How does the temperature of a black body affect its emission and absorption of energy?

The temperature of a black body directly affects the amount of energy it emits and absorbs. As the temperature increases, the black body will emit more energy at all wavelengths and absorb more energy as well. This is why hotter objects appear brighter and emit more radiation than cooler objects.

## 5. What is the significance of a black body emitting as much energy as it absorbs?

This principle is important in understanding the behavior of objects in thermal equilibrium, such as stars and planets. It also provides the basis for concepts such as the Stefan-Boltzmann law, which describes the relationship between the temperature of a black body and the amount of energy it emits. Moreover, it helps scientists to better understand the energy balance of our planet and the role of greenhouse gases in regulating its temperature.