Conduction is quantified as a rate of energy per time. It is dependent on a number of factors including temperature differences, size parameters, and a material property called the thermal conductivity.

$\frac{Q}{\Delta t}=\frac{k A}{L} \Delta T$

Here $\frac{Q}{\Delta t}$ is the rate of energy transfer, measured in SI units as Joules per second. On the right-hand-side of the equation: k (kappa) is a material property called the thermal conductivity, A is the cross-sectional area through which the energy is being transferred, L is the length between the hot and cold side, and $\Delta T$ represents the temperature difference between the hot and cold side. In our discussion we will assume that the hot and cold sides stay at a constant temperature, making the situation in what's called Steady State - which simply means the rate of transfer is constant. An example is maintaining your house at 293 K while the outside maintains 278 K and energy is transfer through the window via conduction. Here A would be the area of the window, L would be the thickness of the glass, k you would look up for glass, and $\Delta T$ would be 293 K minus 278 K, or 15 K.

Convection: Thermal energy, which is a measure of motional energy of microscopic particles, can also be transferred when a higher energy particle physically moves from a higher energy to a lower energy location. In doing so they will have decreased the thermal energy in the hotter location and increased the thermal energy in the colder location. This physical transfer of mass from one location to another is called convection and is the most prevalent form of energy transfer in a gas.

Quantifying convection requires the use of the calculus, which is beyond the scope of this discussion, so conceptual understanding is key. It's important to be able to identify when convection is present and describe the mechanism in terms of particles moving from one location to another.

Radiation: All objects with a temperature greater than 0 K, so all objects... even deep space is around 4 K, radiate electromagnetic energy.

A full blown understanding of this phenomena requires deeper physics (quantum mechanics) than is the scope of our discussion here. But even if we can't understand all the underlying mechanisms, we can still quantify the results. As with conduction, radiation is cast in terms of a rate of energy transfer.

$\frac{Q_{out}}{\Delta t} = \epsilon \sigma A T^4$

In this equation $\epsilon$ is called the emissivity of the object and can be thought of as a material property. $\sigma$ is a constant called Stefan-Boltzmann's constant. A is the surface area of the object and T is the temperature of the object. It's important to note that T must be in Kelvin in this equation. Notice also that the equation says $Q_{out}$, that's because this is the radiation from the object to its environment. But what if the environment also has temperature, like it most definitely will? You must then account for what radiation also comes in to your system - you must find the net radiation in and out to get a complete picture of the change in energy per time. So, the net radiation looks like this:

$\frac{Q_{net}}{\Delta t} = \epsilon \sigma A (T^4-T_e^4)$, where $T_e$ represents the temperature of the environment

Notice that if the object and its environment have the same temperature, the net thermal radiation is zero - just as much energy leaves as enters the object.

Now, take a look at the pre-lecture reading and videos below.

Suggested Supplemental Videos

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