IB Physics Sub-topic B2 Notes

Albedo and emissivity

In Topic B.1, you learned about black body radiation. However, it is purely theoretical and mostly applies to stars, so scientists have created additional terms to describe the radiation of everyday objects. These are: albedo and emissivity.

An object’s albedo (α) is the ratio of its reflected radiation power (P_r) to its total incident radiation power (P₀). This can also be put in terms of intensity, and as such, the formulae are:

$\alpha = \frac{P_{r}}{P_{0}}$

$\alpha = \frac{I_{r}}{I_{0}}$

Sometimes, questions will ask you to calculate the transmitted intensity (I_t) from an object’s albedo. Two handy formulae for this that are not in your data booklet are:

$I_{t} = (1 - \alpha)I_{0}$

$P_{t} = (1 - \alpha)P_{0}$

An object’s emissivity (e) is the ratio of its emission intensity to the emission intensity of a black body. Thus, for non-black body objects, the Stefan-Boltzmann formula is:

$I = e\sigma T^{4}$

$P = e\sigma AT^{4}$

Earth's energy balance

The reason that these aspects of thermal energy transfer are found in this topic is because you need to learn about Earth's energy balance. This can be summarised into three principal sections:

1. The sun produces light that is incident on Earth.
2. This light is partly reflected and partly absorbed.
3. The absorbed light is re-emitted as heat.

Now let's go through this in more detail. The sun’s incident light is termed the solar constant. This is officially defined as the incident solar intensity above Earth’s atmosphere, often given a value of 1360 Wm^-2.

You are expected to calculate this intensity your exam from provided values for the:

1. Sun’s radius = 6.96 x 10⁸ m
2. Distance from the Sun to Earth = 1.50 x 10¹¹ m
3. Sun’s surface temperature, 5780 K. 

When doing this calculation, assume that the Sun is a perfect black body and use the equation:

$P = \sigma AT^{4}$

To find the surface area of the sun:

SA = 4πr²

SA = 4π(6.96 x 10⁸)²

SA = 6.09 x 10¹⁸ m²

Substituting this and other given values into the equation:

P = (5.67 x 10^-8)(6.09 x 10¹⁸)(5780)⁴

P = 3.85 x 10²⁶ W