# Radiation

## Radiation

## Concepts

* Electromagnetic spectrum
* Emissivity
* Absorptivity
* Spectral response
* Planck Distribution
* Planck Law
* Net Radiative heat transfer

## Radiation

* Why do you think radiant heat is important?
* Where do you observe radiant heat?
* What wavelengths are involved?

## Thermal radiation

* What wavelengths do we refer to with thermal radiation?
* Why?

## Using Thermal Radiation

* If we want something to absorb thermal radiation, what properties are necessary?
* If we want something to shed thermal radiation?
* What if we want to use sunlight to warm something?
* What if we want light but not heat?

## Blackbody radiation

* What does the spectrum of radiation look like for the sun?
  * Which part of this is thermal?
* What does the spectrum of radiation look like for the earth?
  * Which part of this is thermal?

## Planck's law

* How do the wavelengths emitted changes as a substance increases in temperature?

### Planck's law

This law relates the intensity of power at each wavelength with the temperature of an object (ideal black-body).

$$B\_\lambda(\lambda, T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda k\_\mathrm{B}T}} - 1}$$

### Stefan-Boltzmann law

* What predicts the total radiant power from a hot object?

### Stefan-Boltzmann law

This law relates the total power emitted to the temperature, surface area, and emissivity of an object.

$$P = A \epsilon \sigma T^4$$

|              |                           |                                                      |
| ------------ | ------------------------- | ---------------------------------------------------- |
| $$A$$        | surface area              | square meters                                        |
| $$\epsilon$$ | emissivity                | dimensionless                                        |
| $$\sigma$$   | Stefan-Boltzmann constant | $$5.67\cdot 10^{-8}$$ W per square meter per K$$^4$$ |
| $$T$$        | temperature               | Kelvin                                               |

### Emissivity

The emissivity is how much radiant power is emitted by a substance relative to an ideal black-body emitter.

If we have two objects with the same surface area and temperature, the object with the higher emissivity emits more radiation.

## Absorptivity

Kirchoff's Law of thermal radiation states that a body in thermodynamic equilibrium, the absorptivity and emissivity are equal.

### Emissive Power

![](https://3265414192-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORGT1Yxp3HKAQ-u%2F-LmGGQ78udBZ3j8aAy-k%2F-LmGGRwGiRpXRbdqVWB-%2FEmissive_Power.png?generation=1565805370606092\&alt=media)

### Emissivities

![](https://3265414192-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORGT1Yxp3HKAQ-u%2F-LmGGQ78udBZ3j8aAy-k%2F-LmGGRwIVe7yh8L7IDpy%2Femissivities-incropera.png?generation=1565805368728122\&alt=media)

### Spectrum

![](https://3265414192-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORGT1Yxp3HKAQ-u%2F-LmGGQ78udBZ3j8aAy-k%2F-LmGGRwKHr8UW0MwacQJ%2Fspectrum-incropera.png?generation=1565805371448912\&alt=media)

### Spectrum

![](https://3265414192-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORGT1Yxp3HKAQ-u%2F-LmGGQ78udBZ3j8aAy-k%2F-LmGGRweTjQev_F0TWLd%2Felectromagnetic-spectrum.jpg?generation=1565805368678689\&alt=media)

### Net Radiative Heat Transfer

$$P = \epsilon \sigma A (T\_1^4 - T\_2^4)$$

### Radiation transfer between surfaces

![](https://3265414192-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORGT1Yxp3HKAQ-u%2F-LmGGQ78udBZ3j8aAy-k%2F-LmGGRwgRIEfz5soBeNH%2Fradiation-transfer.png?generation=1565805371835790\&alt=media)

### Radiation transfer between surfaces

* Why is it colder on clear nights?