Nov 3, 2017 · 3 min read

Professor Goodenough recently provided an update to his “Braga” battery in this this brief interview with Bloomberg New Energy Finance. About halfway through he states:

Goodenough: We’ve found a lot of things you can do with the Braga glass. It’s gone 4,000 cycles with negligible resistance. We have been demonstrating not only can you do that with her glass at room temperature, and in fact we can go well below room temperature. She’s been lighting an LED with this battery charging itself for two years. It runs on ambient heat.

Emphasis mine. This is important. When converting heat to work, there are two important relationships to consider.

The first law of thermodynamics states:

Q - W = ∆U

or the change internal energy of a system is equal to the difference between the heat put in and the work drawn out.

The second law of thermodynamics states that if the system is undergoing a work cycle, the change entropy of a system is greater than or equal to zero, or

∆S ≥ 0

Although Professor Goodenough’s statement is brief, the device,

1. at worst violates the second law, or,
2. at best, is a thermoelectric generator rather than a battery

## Second Law Violation

The second law of thermodynamics is a depressing nightmare in many aspects, but it effectively states this:

One cannot create a field gradient in a system without work/energy input

Another way of phrasing this is the Kelvin-Planck statement:

It is impossible to construct a device which operates on a cycle and produces no other effect than the transfer of heat from a single body in order to produce work.

If one takes the quote above at face value, Professor Goodenough is claiming that a battery, sitting in a room, is drawing heat from its environment to power the LED.

If the room has no temperature gradient, per the Kelvin Plank statement, this is impossible.

## Second Law Upheld….

If we assume from Professor Goodenough’s quote that there is a temperature gradient across the cell in such a way that heat can flow and work can be done, the device becomes a Thermoelectric Stack rather than a battery:

In this case, the heat is directly converted to work, and the battery doesn’t change state. The second case is very unlikely for a variety of reasons: it is difficult to accidentally set up a thermoelectric stack such that you get useful work. I know something about this.

In general there are very small temperature gradients across an entire room, let alone the thickness of a battery, so it is doubtful there is enough energy to power the device. Intentional thermoelectrics powering devices require at least ∆T = 5˚C to generate a few mW, the typical driving power of an LED.

1. If you were in a room with a 5˚C gradient, you’d feel it. It would create pretty significant natural convection (i.e. it would feel really drafty).
2. Just because the 5˚C gradient is available, doesn’t mean you can capture the entire difference. Thermal coupling is very, very hard.

## What’s Going On?

No idea. The first case is clearly impossible. The second case is exceptionally improbable. Something else is going on most likely. Unclear how to propose anything based on what little information there is. Comments welcome.

Written by

## the unfortunate tetrahedron

#### making batteries better one compromise at a time

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