# How to use small variances of temperatures

1. Aug 24, 2013

### exponent137

It is known, that perpetum mobile of the second kind does not exist. This means, ff temperature is everywhere the same, the work cannon be obtained from heat. But temperature is not uniform anywhere.

Let us assume that we have very small cheap heat engines. How much energy can they get from, for instance, one usual room. Are T variations in such a room useful or not, for such theoretical small cheap heat engines?

Is this topic analysed in physics?

2. Aug 24, 2013

### Staff: Mentor

Small temperature differences lead to very small maximal efficiencies, and even worse actual efficiencies.
Within the air in a room, I doubt that you can get a single Joule of useful energy until the temperature is equal everywhere.

As comparison, one kWh is equal to 3.6 million J, and costs some cents.

3. Aug 25, 2013

### exponent137

One Joule is almost nothing. But how do you estimate this Joule? Are anywhere any calculations on this topics?

But time is also important. When we use this Joule, temperature differences arise again very fast.

Last edited: Aug 25, 2013
4. Aug 25, 2013

### Staff: Mentor

Consider two volumes of air with 1m^3 with a temperature difference of 1K. If we cool down one side and heat the other, we get ~600J flowing. At room temperature (~300K), we can extract 1/300 out of this - in an ideal world, we get 2J. This is completely unrealistic, however. First, your volumes of air are separated, you have to transport those 500J of thermal energy without too much loss (=the heat bridge should not be in contact with the environment). Second, mechanical devices won't work with those small temperature differences. You can use the Seebeck effect, but with a difference of 1K you get at most 1mV per contact - good luck transforming this to a useful voltage.
I think an efficiency of a percent is still a optimistic value for the conversion efficiency (relative to the theoretical maximum), so a room with ~50m^3 might give something like 1J.

Using temperature differences between solid materials might be a better approach (especially between the room and the outside), but then you are kind of ruining the purpose of insulations... it might be interesting in spring/fall or (depending on the temperatures) in summer, if you can use the daily temperature cycle.