## Sunday, 6 July 2014

### Metabolic rate, diet efficiency and thermodynamics.

 From Life and Death: Metabolic Rate, Membrane Composition, and Life Span of Animals

This post is based on https://www.facebook.com/richard.feinman.7/posts/667508920000715:-
"When people say the laws of thermodynamics, they usually mean the first law, the law of conservation of energy. However, “conservation of energy” can be a sound bite, at the level of “Einstein said that everything is relative.” You have to know exactly what is being conserved. Precise definitions become very important. One of the many difficulties in understanding thermodynamics is that there are simple principles which seem obvious enough but their import is under-appreciated without a real example.

The first law says precisely that there is a parameter called the internal energy and the change (Δ) in the internal energy of a system is equal to the heat, q, added to the system minus the work, w, that the system does on the environment. (The internal energy is usually written as U so as not to confuse it with the electrical potential).

ΔU = q - w (1)

This is how thermodynamics is taught. To go to the next step you need to understand the idea of a state variable. A state variable is a variable where any change is path-independent. For example, the familiar temperature T and pressure P are state variables. It doesn’t matter whether you change the pressure quickly or slowly. The effect on the system is controlled by the difference between the pressure after the change minus the temperature before the change, that is, ΔP. The usual analogy is the as-the-crow-flies geographical distance, say, between New York and San Francisco. This is a state variable: it doesn't matter whether you fly direct or go through Memphis and Salt Lake City like the flights that I wind up on.

Now, U in equation (1) is a state variable. Any process that you carry out will have a change in U that depends only on the initial and final states. However, q and w are NOT state variables. How you design your machine will determine how much work you can get out of it and how much of the energy change will be wasted. Looking at the biological case, two metabolic changes with the same U have no theoretical reason why they should have the same relative amounts of heat and work, that is, the same efficiency (storing fat as compared to generating heat). Of course, they might but there is no theoretical barrier to difference.

In this, the first law contains the suggestion of the second law. The second law is what thermodynamics is really about.... It is the second law that embodies the special character of thermodynamics. Described by Ilya Prigogine, the Nobel-prize winning chemist and philosopher of thermodynamics, as the first revolutionary science, it is the second law that explains how one diet can be more or less efficient that the other."
Ref: Non-equilibrium thermodynamics and energy efficiency in weight loss diets.

To which I replied:-
"Uncoupling proteins (UCP's) vary ATPADP + heat energy, so as to maintain the human body at 37°C ±3°C, over a wide range of ambient temperatures.

Therefore, "diet efficiency" is varying over a wide range, for all diets."

Followed by:-
"Here's an example:-

To maintain a body temperature of 37°C in an ambient temperature of 20°C, the body needs to generate ~1kcal/min (~69.8W).

If Diet "A" generates 30W due to metabolic processes, UCP's generate an extra 39.8W.

If Diet "B" generates 40W due to lower "diet efficiency", UCP's generate an extra 29.8W.

According to Life and Death: Metabolic Rate, Membrane Composition, and Life Span of Animals:-
"Not all body tissues contribute equally to BMR. For example, ∼70% of the BMR of humans is contributed by internal organs that constitute only ∼7% of body mass..."

As humans must (& can) survive over a wide range of ambient temperatures while being covered with a wide range of clothing while eating a wide range of diets, UCP activity must be capable of being varied from 0 (ambient temperature ≥37°C) to a very high value (swimming in water at 0°C).

Therefore, "diet efficiency" is irrelevant, as UCP's equalise overall efficiency, to equalise the rate of heat energy generation for a given ambient temperature & clothing.