# 89 Cold Weather Survival Time

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



Throughout this unit we have analyzed the rate of heat loss during a cold weather survival situation in which a person is wearing a single layer of thin clothing against an 10 mph wind and a -3 °C air temperature. Our analysis shows that collectively the person would experience a 200 W heat loss rate due to and a 1100 W heat loss rate due to . We also found that using a space blanket to reduce the and would leave only 160 W of heat loss rate due to conduction across the clothing.  The typical person has a of 100 W, but shivering can increase that to 250 W. It would be interesting to know, given these values for and heat loss rate, how quickly body temperature would actually change. In order to answer that question we need to learn about and .

# Human Heat Capacity

In the fight to maintain body temperature the human body gets assistance from the  fact that the body is primarily made of water. The amount of thermal energy required to change the temperature of the body is relatively high compared to other objects of the same because water has a very high (c). Specific heat is a material property that defines the amount of thermal energy removed from one unit mass of the material when it’s temperature changes by one unit of temperature. For example, water has a specific heat of 4186 J/(kg C°) so  4186 J of thermal energy must be removed from 1 kg of water in order for the temperature to drop by 1 C°. Multiplying the specific heat of a material by the mass of the material gives the  (C) of the object. For example, the heat capacity for 80 kg of water would be:  4186 J/(kg C°) x 80 kg = 334,880 J/(C°), meaning that 334,880 J must be removed to drop the temperature of 80 kg of water by 1 C°.

### Reinforcement Exercises

Now that we know how to calculate we are ready to calculate the amount of energy required to change the temperature of the body by a dangerous amount. We just multiply the (m) by the (c) to get , which we then we multiply by a dangerous temperature change ( ) to get the required (Q). This entire process can be summed up by the equation:

(1) Notice that if the temperature is dropping then final temperature is less than the initial temperature so will be negative, which makes negative, indicating that thermal energy is leaving the object. The equation works for heating as well as cooling because in that case and will be positive indicating that thermal energy is entering the material.

### Reinforcement Exercises

The following chart provides values for various substances. Notice the relatively high specific heat of water.

 Substances Specific heat (c) Solids J/kg⋅ºC kcal/kg⋅ºC Aluminum 900 0.215 Asbestos 800 0.19 Concrete, granite (average) 840 0.20 Copper 387 0.0924 Glass 840 0.20 Gold 129 0.0308 Human body (average at 37 °C) 3500 0.83 Ice (average, -50°C to 0°C) 2090 0.50 Iron, steel 452 0.108 Lead 128 0.0305 Silver 235 0.0562 Wood 1700 0.4 Liquids Benzene 1740 0.415 Ethanol 2450 0.586 Glycerin 2410 0.576 Mercury 139 0.0333 Water (15.0 °C) 4186 1.000 Gases Air (dry) 721 (1015) 0.172 (0.242) Ammonia 1670 (2190) 0.399 (0.523) Carbon dioxide 638 (833) 0.152 (0.199) Nitrogen 739 (1040) 0.177 (0.248) Oxygen 651 (913) 0.156 (0.218) Steam (100°C) 1520 (2020) 0.363 (0.482)


### Everyday Examples: Cold Weather Survival Time

Applying the previous equation to the human body we can estimate how long it would take body temperature to drop from a normal 37 °C down to the edge of moderate at 33 °C in the example survival situations discuss so far in this unit. Let’s use relatively common human of about 80 kg and the average of human tissue of 3470 J/(kg C°). First we find the loss required for the temperature drop: We know that in our example of a 10 mph wind and a -3 °C air temperature we found that a person with thin clothing and no space blanket experienced 1100 W of convective heat loss and 200 W of radiative heat loss for a total of 1300 W.  If the person was shivering then their would be roughly 250 W. This person would have a 1150 W thermal power deficit, which means they lose 1150 Joules of thermal energy each second. Dividing the dangerous heat loss we calculated above by the thermal power deficit gives us the time required to lose that much heat: Dividing the 900 by 60 (s/min), we see that would be reached in only 14 minutes.   In reality, the rate of heat loss depends on the temperature difference so the rate of heat loss would not be constant, but instead it would slow a just bit as body temperature decreased. In our example case the 40.9 difference between the body temperature and environment temperature changed by only  about 3 (seven percent). Ignoring this effect gives a reasonable for the time until moderate hypothermia. The next two sections will address this approximation and allow us to calculate the time required for more significant temperature changes.

# Rates of Body Temperature Change

The rate at which thermal energy is transferred out of the body depends on the difference in temperature between the body and the environment. As the body cools closer to the environmental temperature the rate will decrease. In the previous example we ignored this reality and assumed that the cooling rate was constant, which was reasonable because we only examined a very small temperature change. For our example situation we found that mild would be reached in only twenty minutes. The graph below was produced by calculating the body temperature while accounting for a cooling rate that depends on the temperature difference. This was done using a numerical model:

1. calculating a heat transfer rate for the initial body temperature due to both and
2. using that heat transfer rate to calculate the amount of transferred over a relatively short time interval
3. using the amount of transferred to calculate a resulting reduction in body temperature
4. calculating a new body temperature by subtracting the reduction in body temperature
5. repeat 1-5 until temperature was well beyond survival temperature, keeping track of the temperatures and times to make the graph

We see that the time to mild is actually more like 30 mins. We also see that severe hypothermia could set in after less than an hour and the minimum survivable temperature could be reached in under two hours. For the purpose of these calculations we assumed a of 250 W while shivering, and that shivering stops when the body reaches 30 °C, at which point thermal power returns to 100 W.  We also assumed the that thermal power dropped to zero when body temperature reached 21 °C. 