In the X-Files TV series, a man is injected with a chemical that freezes him. When defrosting, his bodystarts producing exothermic reaction that sets him on re. At normal metabolic rate, this reaction wouldtake at least 4 days 15 hours and 24 minutes. In the time scale of the show the energy required to heatthe body would be 9.9 x 105 W

Harris, Ben G.S.

Harrison, Zoe

Holesinsky, Tomas

Mandhai, Soheb

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalP2 4 Not So Spontaneous CombustionT .Holesinsky, Z. Harrison, S. Mandhai, B. G. S. HarrisDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHNovember 3, 2016AbstractIn the X-Files TV series, a man is injected with a chemical that freezes him. When defrosted, his bodystarts producing exothermic reaction that sets him on fire. At normal metabolic rate, this reaction wouldtake at least 4 days 15 hours and 24 minutes. In the time scale of the show the energy required to heatthe individual would be 9.9 x 105 W.IntroductionX-Files is a sci-fi series from the 90s where themain characters often encounter unexplainableor uncommon phenomena. In one episode, a manis injected with a serum that freezes him andupon raising his temperature to normal valuehis cells begin exothermic reaction. This causeshim to combust in a matter of seconds. We in-vestigate how long it would take for a normalmetabolic rate to produce sufficient energy andwhether it is feasible for the body to produce thisamount of energy in such a short period of time.TheoryIn order to estimate the combustion of humans,we look at similar phenomena of spontaneouscombustion. In this myth one theory suggeststhat fat in human body acts as wax in a candle,which allows this event to occur [1]. We estimatethat in order for an individual to incinerate, heneeds to reach the auto-ignition temperature offat: 553.15 K for animal fat [2].To evaluate the required energy we used thecalorimetric equation [3]; Equation 1:Q = mc (Tf − Ti) (1)We assume the mass of the person ,m, to be 70kg. The initial and final body temperatures, Tiand Tf respectively, to be 309.15 K and 553.15K. The specific heat capacity, c, of a human bodyis 3470 J kg−1K−1 [4].The rate at which humans emit heat, Pr, is100 W [5]. We idealise the conditions and as-sume the person does not lose any energy to hissurroundings. The time it would take to reachauto-ignition temperature can be found with [3];Equation 2:t =QPr(2)Investigating further, we decided to calculatehow the amount of fat in the body affects the en-ergy requirements for auto-ignition. Simplifyingthe situation, we assume that the human bodyconsists solely of fat and water.Thereupon, we find that the heat capacitiesof fat and water are cf = 2348 J kg−1K−1 andcw = 4186 J kg−1K−1, respectively [6][3]. Wethen calculate the heat required based on thepercentage of fat and water in body. This isdemonstrated by Equation 3;.P2 4 Not So Spontaneous Combustion, November 3, 2016Qt = xQf + yQw (3)Where Qf is heat for fat, Qw is heat for wa-ter, x is the fraction of fat in the body, y is thefraction of water in the body, and Qt is the totalheat required.We then plot the relationship between Qt andt to find that the higher the amount of fat the lessenergy is required. The red circle indicates theresult found with usage of specific heat capacityof the body.Figure 1: The time taken to heat up the body to au-toignition point with changing heat based on the amountof fat and water in the body.We estimate the time it takes for the individ-ual to ignite in the episode as 60 s. Then we sub-stitute into Equation 2 rearranged for Pr. Usingthe energy from the specific heat capacity of thehuman body we evaluate the power which themetabolism would have to produce autoignitionin this time.DiscussionThe energy required to increase temperature ofa person using the specific heat capacity of bodywas found to be 5.9 x 107 J. The time it wouldtake for the body to produce such heat at rateof 100 W is about 6 days 20 hours and 38 min-utes. From Figure 1 the specific heat of bodyapproximates a ratio of 62% water and 38% fat.Furthermore, even if the individual consisted offat it would take 4 days 15 hours and 24 minutesto heat him up.In the scenario of the person autoigniting in60 s we need to supply power of 9.9 x 105 W. Asa comparison, the power consumed by a kettle isbetween 1200 and 3000 W [7].ConclusionBased on our evaluation of the problem we be-lieve enough evidence is presented to prove thatsuch a reaction cannot occur. Even in idealisedconditions where no heat is lost to the surround-ings, the time required for sufficient heat to beproduced is in the order of days. In terms ofpower production, the body would need to turninto a small power plant to produce such power.References[1] http://www.brianjford.com/a-1208-NSci-SHC.pdf (19/10/2016)[2] http://www.vho.org/tr/2004/1/Mattogno64-72.html (19/10/2016)[3] Tipler, P. A. Tipler and G. Mosca, PhysicsFor Scientists and Engineers With ModernPhysics, (W. H. Freeman and Company, NewYork, 2008)[4] http://www.engineeringtoolbox.com/human-body-specific-heat-d_393.html(19/10/2016)[5] http://www.physlink.com/education/askexperts/ae420.cfm (19/10/20116)[6] https://www.itis.ethz.ch/virtual-population/tissue-properties/database/heat-capacity/ (19/10/2016)[7] https://www.daftlogic.com/information-appliance-power-consumption.htm (19/10/2016)

P2_4 Not So Spontaneous Combustion

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P2_4 Not So Spontaneous Combustion

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