School of Design and Engineering
Kanbar College of Design, Engineering & Commerce
Philadelphia University
A report on
Thermodynamics of a Human Body
Course:
MENGR 407 Thermodynamics and Heat Transfer I
Students:
Brendan Murray
Leigh Krauser
Fall 2013
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Abstract
Our main objective for this project was to study the thermodynamics of a
human body and determine the number of calories needed for different
environments. It is common knowledge that an average person needs to consume
around 2000 calories per day to stay healthy, but we wanted to research exactly
how this number is computed and how different atmospheric temperatures can
affect it. Convection, radiation, and the metabolism are the ways our body loses
energy while food intake is our way of gaining energy. Once calculating these
three topics, we added them together to find the total required food energy. In
order to see exactly how much the outdoor temperature affects this number, we
made our calculations with reference to various different locations. Hawaii,
Alaska, and Pennsylvania were the locations we used. After completing our
research and calculations, we had a much better understanding of how the human
body transfers heat to the environment while maintaining homeostasis. We also
learned a lot about convection, radiation, metabolism, and how different physical
activities and different foods affect how the human body works.
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Introduction/Problem Statement
The first goal was to understand how the human body operates. The human
body, just like any other energy-producing machine, operates as a closed system
where the amount of energy intake is equal to the energy it produces. While most
machines are fueled by electricity, gas, coal, etc., the human body’s source of fuel
is Calories. Most food products that we buy and consume have food labels which
conveniently display the amount of calories in that particular food item. However,
what most people don’t know is that calories are also a form of heat transfer. We
usually think of joules when it comes to units of heat transfer. Thankfully, we were
able to convert all of our heat transfer calculations into calories by using the
equation 1 calorie is equal to 4.184 joules. There was one last conversion we
needed to make before setting up our calorie intake equation. The calories you see
on food labels are not the same as the calories that you are burning. The calories
that we receive from food are actually kilo-calories. Therefore, we took our final
sum of the convection, radiation, and metabolism factors and divided it by 1000 to
give us the required calorie intake.
As previously stated, the human body burns calories in a variety of ways.
There are multiple chemical processes going on in our body at every hour of the
day. Even when we are sleeping, we are burning calories. The main forms of
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energy usage that we will be studying are convection, radiation, and metabolism.
There are a few other ways in which we burn energy including breathing and the
defecating of human waste, but our research led us to the conclusion that both of
these processes were negligible. The three topics we focused on all had very
different processes with different factors to consider.
Luckily, we learned a lot about the convection process this year in our
Thermodynamics and Heat Transfer I class. Technically, convection is the energy
transfer between a solid surface and an adjacent gas or liquid by the combined
effects of conduction and bulk flow within the gas or liquid. When a gas is
warmed, it loses some density and begins to rise. The full convection cycle of air
occurs when the gas is the cooled back to a liquid and sinks back down. A good
example of convection is a hot air balloon which heats up gas to make the balloon
rise then cools it back down to safely land back on the ground. Convection can be
calculated using Newton’s Law of Cooling. This equation is Q=h*A*(Ts-Ta),
where A is the surface area (of a human body), h is an empirical parameter called
the convection heat transfer coefficient, Ts is the surface temperature (skin
temperature), and Ta is the atmospheric (or air) temperature.
The process of thermal radiation was also covered in our Thermo class this
year. Thermal radiation is energy transferred by electromagnetic waves (or
photons) and is an application involving net radiation exchange between two
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different sized surfaces with different temperatures. The best example of this is the
sun heating the earth. The sun (much large surface area and higher temperature)
sends electromagnetic waves, called rays, down to the earth (smaller surface area
and lower temperature) which heats it up. The total amount of radiation is given by
the equation Q=ε*σ*A*(Ts4-Ta4), where ε is a property of the surface called its
emissivity, σ is the Stefan-Boltzman constant, A is the surface area (of a human
body), Ts is skin temperature, and Ta is air temperature.
There is one last process to consider and that is metabolism. Metabolism is
the total amount of energy the body uses to complete its basic everyday functions.
Although some people may think that we are only using energy during strenuous
activities, we are actually using energy every second of the day. Simple proceses
such as breathing, pumping blood throughout the body, and digesting food are just
a few examples. Since all of these functions are using energy (and releasing heat),
the body must regulate this and stay at a comfortable living temperature. The
human body actually does a fantastic job of regulating internal body temperature.
Although skin temperature can vary greatly depending on the external conditions,
the vital organ temperature amazingly never varies more than a couple degrees
(unless you have a fever). The amount of energy burned through metabolism is
referred to as the BMR (Basal Metabolism Rate).
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Obviously, the types of food you eat and types of daily activities you
perform will have an affect on how your body operates daily as a machine. The
physical activities a person performs can be considered a sub-category of BMR.
The standard BMR rates are usually calculated for a person at rest throughout the
entirety of the day. However, we have found data that determines the amount of
energy burned due to various activities. We looked up values for sleeping,
standing, sitting, walking, driving, cleaning, playing volleyball, jogging, and
skiing. As for the types of food we consume, that is more related to energy intake
rather than the burning of energy and is a topic that we won’t be covering in this
project.
Problem Solving
Our main goal is to determine the calorie intake of an average person.
Simply stated, F=C+R+BMR, where E is the caloric energy needed from food, C is
energy lost due to convection, R is energy lost due to radiation, and BMR is energy
lost due to metabolism. Two of these, convection and radiation, are affected by the
temperature of the surrounding air, while BMR is affected by the level of physical
activity performed. Although we will briefly discuss BMR and how it is affected
by certain physical activities, our main objective is to show how different
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temperatures will affect calorie intake through convection and radiation. Again, we
will be comparing temperatures in three different parts of the country to portray
this.
We started about by trying to solve for convection since it was one of the
two processes dependent on air temperature. As previously stated, Q=h*A*(Ts-Ta),
where A is the surface area (of a human body), h is an empirical parameter called
the convection heat transfer coefficient, Ts is the surface temperature (skin
temperature), and Ta is the atmospheric (or air) temperature. After reading through
various websites, we estimated that the average surface area of a human body is
1.8 m2. The heat transfer coefficient (h) can be calculated using the equation
h=1.22*(Ts-Ta).299. Since both convection and radiation required skin temperature
and air temperature, we made skin temperature a constant value (90°F which is
306°C) in order to compare it with temperatures at our three different locations
(Ts). We calculated all of our values using average winter temperatures in Hawaii,
Pennsylvania, and Alaska. Once we found these temperatures, we converted them
into Kelvin and plugged them into our equation to find Q. This value was in a unit
of BTU/hr. Our intended units are food calories per day. In order to achieve this
unit, we first had to convert Watts/hr to kilo-joules per hour, then kilo-joules per
hour to kilo-joules per day, then finally kilo-joules per day to food calories per day.
Refer to our excel sheet for all equations and conversions.
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The next step was to calculate radiation. Again, the total amount of radiation
is given by the equation Q=ε*σ*A*(Ts4-Ta4), where ε is a property of the surface
called its emissivity, σ is the Stefan-Boltzman constant, A is the surface area (of a
human body), Ts is skin temperature, and Ta is air temperature. Through research,
we found that human skin has an emissivity level of 90%. We used the same
surface area as we did in convection (1.8 m2). The Stefan-Boltzman constant is
required for calculating radiation and is equal to 5.67*10-8 W/(m2*T4). As
previously stated, we used a constant number for skin temperature and three
different measurements for air temperature. Like we did in convection, we had to
convert Watts/hr to kilo-joules per hour, then kilo-joules per hour to kilo-joules per
day, then finally kilo-joules per day to food calories per day. We found that
radiation takes up a greater percentage of total energy usage than convection did.
As expected, a greater difference between skin temperature and air temperature
resulted in a greater amount of food calories required for homeostasis. Again, refer
to our excel sheet for all equations and conversions.
Finally, we arrive at metabolism, which greatly affects our calorie intake but
is not dependent on air temperature. We decided that the best way to calculate our
total metabolism was to break down physical activity by the hour. Different levels
of activity require different amounts of energy usage. Even sleeping requires a
different amount of energy than sitting. This is because breathing patterns are
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slower and the heart pumps blood to the rest of the body at a much more relaxed
rate. We found energy usage values for sleeping, standing, sitting, walking,
driving, cleaning, playing volleyball, jogging, and skiing. Sleeping is measured at
75 Kj/hr, standing is 480 Kj/hr, sitting is 300 Kj/hr, walking is 840 Kj/hr, driving a
car is 320 Kj/hr, cleaning is 1500 Kj/hr, playing volleyball is 1500 Kj/hr, jogging is
2070 Kj/hr, and skiing is 1410 Kj/hr. We then assigned the amount of hours we
think that an average person spends on these activities (or activities similar to the
examples). Through research, we found that an average person sleeps 8 hours per
day which was a good starting point to work off of. We made a chart to compare
the amount of calories needed for an active person (athlete) versus an average
person who performs little to no strenuous activities. In extreme cases, professional
athletes who are performing strenuous activities for a larger portion of the day, like
Michael Phelps, need around 12,000 food calories per day!
Conclusions
After calculating our 3 processes and adding them up to find our total
amount of food calories needed, we were pretty satisfied with our result. As
expected, a greater difference in temperature between skin and air resulted in a
great amount of calories needed. That being said, we realize that we made a lot of
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assumptions and there were many factors we were unable to account for. For
instance, we were unable to enough credible data to account for wind. Wind chill
factor can affect air temperature. Wind is also a form of convection. One big
assumption that we made is that there was no wind at the three locations. In this
case, we would be calculating free convection. Wind is a type of forced convection
and would have an effect on our convection equations. We also decided to
disregard humidity. The level of humidity would affect both our radiation and
convection equations. A more humid environment would make it more difficult for
water vapor to evaporate off of our skin, which in turn would use up more energy.
Aside from convection and radiation, there were also some things we didn’t
take into account when setting up our metabolism equations. Our data we compiled
for different physical activities were taken straight from a website and our purely
averages among most people. We were unable to factor in many variables for our
BMR. For example, the height, weight, and body composition of a person
obviously have an effect on the amount of energy burned during physical activity.
Also, less obvious variables such as stress level, age, and health (if a person is sick
or has a fever) will also have a significant impact. And lastly, we previously stated
that temperature would only affect our convection and radiation values, which is
incorrect. Performing a strenuous activity in a very cold or very hot environment
will burn more energy than performing these same activities near room
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temperature. Although we found research backing this up, were unable to find
enough convincing calculations to justify putting it into our equation.
There were many possible errors that could have been made during this
project. First of all, the majority of time we put into this project was towards
finding the right equations to give us the expected the amount of food energy
required. There were no actual physical experiments that we could do to help our
research. Finding out how the body releases energy through convection, radiation,
and metabolism was the easy part. However, sorting through multiple websites to
come up with the most accurate energy usage equations was extremely difficult.
This is where the bulk of our errors will come from. A lot of online material is
either too vague, outdated, or just incorrect. The rest of the errors will come from
the variables which we neglected to account for (wind, humidity, breathing,
physical activities at different temperatures, body composition, etc.).
In the end, we were able to find different calorie intakes at different
environmental locations which was our main goal. However, the effects of
convection and radiation had a much smaller impact than we expected. The
convection effect in Alaska was 1200% more than in Hawaii, which we were
pleased with. The overall impact of convection and radiation varies depending on
location but can take up as much as a quarter of one’s daily calorie intake. We
found that the major reason for a person needing more food calories is due to
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physical activity level, not air temperature. People that perform more strenuous
activities on a daily basis will sometimes need double the amount of food an
average person would need (or in Michael Phelps case, around 6x more). Our
results showed that convection and radiation can make up to a 25% difference in
food calories needed. We definitely learned a lot about how the human body acts
as a machine and how it is no secret that more physical activity leads to the largest
amount of calories burned.
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Works Cited
http://djelatnici.unizd.hr/~mdzela/nastava/EnvironmentalPhysics.pdf
http://mb-soft.com/public2/humaneff.html
http://www.weather.com/outlook/travel/vacationplanner/compare/results?from=vac_compar
e&clocid1=USAK0012&clocid2=USPA1277
http://www.webmd.com/diet/features/estimated-calorie-requirement
http://djelatnici.unizd.hr/~mdzela/nastava/EnvironmentalPhysics.pdf
https://www.boundless.com/physics/thermodynamics--3/the-first-law-ofthermodynamics/human-metabolism/
http://www.biofizyka.sum.edu.pl/lab/lab5.prn.pdf
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