# Spontaneous Exhaustion of Heat

According to the Second Law of Thermodynamics, any real process leads to an increase in entropy. In fact, left on it’s own, any system will spontaneously undergo processes that lead to higher entropy. For example a warm object in a cold environment will spontaneously transfer thermal energy to that environment.

Everyday Example: Exhausting Heat

We claimed that a warm body spontaneously exhausts heat to the environment. The person + environment system is isolated (no outside energy sources) so if calculate that exhausting heat will increase the total entropy of the system then it will happen spontaneously.

To get the total entropy change of the body + environment we need to add up the entropy changes for each:

We can use the equation for entropy change at constant temperature that we introduced in the last unit.

So then we have:

The heat gained by the environment was lost by the body, so the heats are actually the same amount, but the heat for the body is negative:

The environment entropy increases (the first term is positive) and the body entropy decreases (second term is negative). However, we know that the second term is actually smaller because the same heat value is divided by larger number, (body temperature is higher than the environment temperature). With a smaller negative term and larger positive term, the overall entropy is positive, which means the body will spontaneously exhaust heat to this environment.

Everyday Example: Irreversible Sweating

Transfer of thermal energy away from the body by evaporation of sweat is also a spontaneous process, meaning the process is irreversible. Imagine trying to run around and grab all the water vapor molecules and shove them back into the liquid on our skin and then make those water molecules collide with skin molecules in just the right way to conduct thermal energy back into your body! Good luck. If the process could be reversed, the net entropy[change would be zero, but that is not a real possibility.  Any real process increases the entropy because it is irreversible at some level, meaning energy is further dispersed throughout the system without a realistic opportunity to put it back where it was. Even if you could reverse the evaporation process as we just described, the exhaust heat you released during that running around would decrease the concentration of energy in your body and disperse it throughout the room. The system, which includes you, would not have returned to the original conditions at all. In fact, the total entropy would have increased by even more!  As you ran around grabbing molecules you would have converted more chemical potential energy to thermal energy, more sweat would have evaporated, and you would then have to chase those molecules down as well, and so on forever–you could never win! We can’t keep the entropy of the universe from increasing.

The body relies on that spontaneous transfer of thermal energy in order to exhaust heat to the environment, which seems nice because it happens automatically. However, those spontaneous process are not under our control, they cannot be stopped or reversed, which can be problematic. Under the right low-temperature conditions the exhaust rate can be  higher than the thermal power of the body and the total thermal energy will decrease and temperature will drop (hypothermia). High temperature conditions can cause an exhaust rate that is too low, or even negative (heat flows into the body), and then hyperthermia occurs. While we can’t stop or reverse heat transfer, we can slow it down by understanding the microscopic mechanisms of heat transfer.

# Preventing Hypothermia

## Shivering

 Stage Core Body Temperature °C Symptoms Mild Hypothermia 35°-33° shivering, poor judgment, amnesia and apathy, increased heart and respiratory rate, cold and/or pale skin Moderate Hypothermia 32.9°-27° progressively decreasing levels of consciousness, stupor, shivering stops, decreased heart and respiratory rate, decreased reflex and voluntary motion, paradoxical undressing. Severe Hypothermia < 26.9° low blood pressure and bradycardia, no reflex, loss of consciousness, coma, death

[1]

When the thermal power is less than than the heat loss rate then the body will lose thermal energy over time and body temperature will drop. The only options for preventing hypothermia are slowing down the heat loss rate and/or increasing the thermal power. You can fight off hypothermia by doing additional work, such as jumping around, because the body is inefficient so most of the chemical potential energy used to do the work actually becomes thermal energy that can replace what was lost as heat. Shivering is your body’s way of subconsciously forcing you to take this approach and signifies a mild stage of hypothermia. However, this strategy will only be successful until you have used up your readily accessible supply of chemical potential energy. Basically, as you get tired this method will fail. The overall chemical to thermal energy conversion rate can be supplemented by technology such chemical hand/foot warmers and battery powered heated clothing, but in most situations will your body does the bulk of the conversion. Eventually these supplemental energy sources will also run out and body temperature will continue to drop. Moderate hypothermia is indicated by the end of shivering and increased mental confusion, possibly including hallucinations. Severe hypothermia leads to loss of consciousness and if not treated, eventually death.[2]

### Everyday Example: Human Thermal Power

The typical daily intake of chemical potential energy required by the human body is 2000 Calories. Nearly all of that chemical energy is converted to thermal energy. Therefore we can reasonably approximate the thermal power () of the human body to be roughly 2000 Calories/day. Remembering that food Calories with a capitol C are actually kcals and that 4.186 Joules are in one calorie, we can apply unit conversion to estimate the human thermal power in SI units of Watts.

Shivering can boost the thermal power up to about 250 W, which is 2.5x greater than the thermal power calculated above. In other words, shivering for 24 hrs would require 4500 Calories.

## Slowing Heat Transfer

Materials designed to slow the heat transfer rate, or thermal insulation, can be used to help prevent hypothermia by ensuring the heat exhaust rate is not lower than the thermal power. There are four ways that heatis transferred away from the body.

1. Conduction
2. Convection
4. Evaporation

The following chapters will discuss these mechanisms and the strategies used to increase or decrease the rate of each in order to maintain constant body temperature.

### Everyday Examples: Insulation

My father was a bush pilot in Alaska. When I was about 13 years old we were landing on a lake in our hometown and found two teenagers clinging to their overturned canoe. The first boy had a stocky build and second was tall and thin. Both boys were wearing cotton clothing, which did not provide much insulating value in the water. The first boy climbed onto the float and into the plane with some assistance, the thin boy was unable to move and was dragged out of the water just before losing consciousness as we rode back to shore. We later learned that the thin boy had reached the third stage of hypothermia and was likely only minutes from death. There were actually three reasons why being thin was a disadvantage in this situation: The thin boy had less body mass so his temperature changed more with each quantity of heat lost, he also had thinner layers of tissue to provide insulation and reduce the rate of heat loss, and finally, he had less chemical potential energy stored up for conversion to thermal energy through shivering. In the following chapters we will learn in more detail how each of these factors contributed to the dramatically different conditions in which the boys were found.

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