Problem 5: Another friend of yours has a Kickstarter idea: she wants to design a
ID: 583292 • Letter: P
Question
Problem 5: Another friend of yours has a Kickstarter idea: she wants to design a small heat engine that charges your smartphone using body heat. She asks you, the resident physics expert, work. (a If body temperature is 37oC and room temperature is 20°C, what will be the maximum efficiency this can reach? (b) A human outputs about 2000 kcal of heat per day. Convert this to calories per second. (c) At most, a small device could only hope to harvest 1% of a person's heat output. In cal/s, how much heat would be supplied to the device per second? (d) Using your result from parts (a) and (c), what is the maximum power (in cal/s) that could be supplied to the phone? (e) Convert your answer from part (d) to J/s. (Note: 4.184 A typical smartphone needs 40000 J to become fully charged. Using your friend's device, what is the minimum time it will it take to charge a phone?Explanation / Answer
a) Tc = 20 C = 20 + 273 = 293 K
Th = 37 C = 37 + 273 = 310 k
efficiency, e = 1 - Tc/Th
= 1 - 293/310
= 0.0548
b) out put = 2000 kcal/day
= 2000*10^3 cal/(24*60*60 s)
= 16.34 cal/s
c) heat supplied to the device = 16.34*0.01
= 0.1634 cal/s
d) heat supplied to the phone = e*0.1634
= 0.0548*0.1634
= 0.00895 cal/s
e) heat supplied to the phone = 0.00895*4.184 J/s
= 0.03746 J/s
f) time taken = 40000/0.03746
= 1067666 s
= 296.6 hours
= 12.36 days