|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 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 rate due to 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 , 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 the human body gets assistance from the fact that the body is primarily made of water. The amount of 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°.
Calculate the heat capacity of 150 kg of water.
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:
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 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.
Calculate the required to raise the temperature of 150 kg of water from 14 °C to 40 °C, as is necessary for a typical bath.
Calculate the cost of one bath when using an electric water heater and energy is sold at 12 cents per . Assume the water heater is 100% at converting electrical energy into and transferring that to the water as .
One bath per day would cost how much each month?
The following chart provides values for various substances. Notice the relatively high specific heat of water.
|Substances||Specific heat (c)|
|Concrete, granite (average)||840||0.20|
|Human body (average at 37 °C)||3500||0.83|
|Ice (average, -50°C to 0°C)||2090||0.50|
|Water (15.0 °C)||4186||1.000|
|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 deficitm meaning that they lose 1150 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 s by 60 (s/min), we see that would be reached in only 14 minutes. In reality, the depends on the difference so the heat loss rate would not be constant, but instead it would slow a bit as body temperature decreased. In our example case the 40.9 C° difference between the body temperature and environment temperature changed by only about 3 C° (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.
We found previously that a person in wet cotton, but with a space blanket would experience an 1100 W heat loss rate, giving an 850 W deficit. Calculate the time to moderate hypothermia in this situation, in minutes.
Calculate the time in minutes to moderate hypothermia for an 80 kg person wearing wet down in the mountain climbing example at the start of this chapter, for which the rate of heat loss was 5600 W.
Calculate the time in minutes to reach severe hypothermia body temperature (see hypothermia chart) for a person in the same situation as the previous everyday example, but with a mass of only 60 kg.
Rates of Body Temperature Change
The rate at which 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:
- calculating a for the initial body due to both and
- using that e to calculate the amount of transferred over a relatively short time interval
- using the amount of transferred to calculate a resulting reduction in body
- calculating a new body temperature by subtracting the reduction in body temperature
- 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.
Approximate body temperature vs. time for an 80 kg person in 25 °F air temperature and 10 mph wind (-3 °C , 4.5 m/s). For the purpose of these calculations we assumed a thermal power of 250 W while shivering, that shivering stops at 30 °C at which point thermal power returns to 100 W, and that thermal power dropped to zero below 21 °C. Minimum survivable body temperature and record low body temperature survived were found at “How Cold Can a Body Get” by Ali Venosa, Medical Daily and “Frozen Alive” by Peter Stark, Outside Magazine.
Modeling how body temperature changes with time under different insulation and temperature conditions allows forensic investigators to measure a body’s temperature and work backwards to determine the time at which body temperature started to drop from normal. In this way time of death can be determined (unless of course the person was hypothermic or hyperthermic before death).
- Adapted from "Web-based hypothermia information: a critical assessment of Internet resources and a comparison to peer-reviewed literature" by M Spencer, Jeremy & Sheridan, Scott, Perspectives in public health, 135(2) · February 2014 ↵
- "Nutritional Needs In Cold And In High-Altitude Environments: Applications for Military Personnel in Field Operations" byAndrew J. Young, Michael N. Sawka and Kent B. Pandolf, National Center for Biotechnology Information, National Institutes of Health ↵
- OpenStax, College Physics. OpenStax CNX. Nov 8, 2018 http://firstname.lastname@example.org ↵
- Engineering ToolBox, (2001). [online] Available at: https://www.engineeringtoolbox.com [Accessed 27 1 2019] ↵
The condition of having a body temperature well below the normal range.
the amount of heat (thermal energy transferred due to a temperature difference) that leaves an object per unit time
Electromagnetic radiation spontaneously emitted by all objects with temperature above absolute zero.
transfer of heat due to the movement of fluid molecules driven by external factors other than thermal expansion.
Increase in rate of heat loss from objects that are warmer than air caused by the flow of air across the object surface.
the process by which heat or directly transmitted through a substance when there is a difference of temperature between adjoining regions, without movement of the material
rate at which chemical potential energy is converted to thermal energy by the body, batteries, or heat engines. Also, rate at which thermal energy is converted to electrical energy by a thermal power plant.
A material property that determines the amount of energy required to raise the temperature one mass unit of the material by one temperature unit.
The amount of energy required to raise the temperature of an object by one temperature unit.
a measure of the average kinetic energy of the particles (e.g., atoms and molecules) in an object, which determines how relatively hot or cold an object feels
energy stored in the microscopic motion of atoms and molecules (microscopic kinetic energy)
a measurement of the amount of matter in an object made by determining its resistance to changes in motion (inertial mass) or the force of gravity applied to it by another known mass from a known distance (gravitational mass). The gravitational mass and an inertial mass appear equal.
An amount of thermal energy transferred due to a difference in temperature.
ratio of useful work performed to total energy expended
International standard (SI) unit of Energy
a rough value obtained without making a measurement by using prior knowledge and assumptions.
amount of thermal energy transferred into our, out of an object as heat, per unit time