I'm really curious about this and haven't been able to find a formula to calculate the types of voltages I could generate based on differences in temperature. An example of interest is The PowerPot which can charge a phone by boiling water over a campfire (snow would work better due to a larger difference).
I know that the average temperature of a campfire (well stocked) is roughly $1000^\circ C$ and through several Google searches I have very roughly estimated the average surface temperature of the planet at $15^\circ C$ and am going with my original educated guess that the temperature of the water used is roughly $20^\circ C$. This is a massive difference in temperature and I wonder if it's mandatory.
With some further research into the topic, I have found a formula which hasn't been 100% helpful.
Seebeck Coefficient
You can read more on this one here; however, to sum it up:
$$S = -\frac{\Delta V}{\Delta T}$$
Where $\Delta V$ is the voltage difference between the hot and cold sides, and $\Delta T$ is the temperature difference. The negative sign is from the negative charge of the electron and the conventions of current flow.
Is the difference in temperature always required to be this drastic? How do I calculate the correct difference in temperature needed to achieve a specific voltage output? How do I calculate $\Delta V$ when both sides are ambient temperatures instead of physical (can touch it) objects?
