As you read the problem, your brain is consuming about 22W of power. a) How many

Question

As you read the problem, your brain is consuming about 22W of power.
a) How many steps with a height of 21cm must you climb to expend a mechanical energy equivalent to one hour of brain operation?
b) A typical human brain, which is 77% water, has a mass of 1.4kg. Assuming that the 22W of brain power is converted to heat, what temperature rise would you estimate for the brain in one hour of operation?
Ignore the significant heat transfer that occurs between a human head & its surroundings, as well as the 23% of teh brain that is not water.

Explanation / Answer

Part A) Step 1: Find how many joules your brain uses in an hour. Knowing that our brain runs at 22 w or 22j/s we then just need multiply that by how many seconds are in an hour. 60m/hr 60s/m so 60*60 = 3600 22j/s * 3600s = 79200 j Step 2: Knowing how many joules our brain uses in an hour we can now set that equal to the mechanical potential energy. E = mg where E is the number of joules our brain uses m is the average mass for an adult human (70 kg) and g (9.8m/s) is the acceleration due to gravity and h is the height. Now if we solve for h we get h=E/gm 79200/ (70*9.8) = 115.45m. Step 3: Using this height we than can found how many 21cm stairs we must climb to get to that height or that potential. Remember To convert units’ cm to m 21cm = .21m. 115.45m/.21m = 549.771 or 550 stairs. Part B) Step 1: Having the joules that the brain uses in an hour we can now convert that to calories. Remember that 1 calorie can heat up one gram of water 1 degree C. 1 joule = .25 calories 79200j * .25 cal/j =19800 cal Step 2 If our brains have a mass about 1.4 kg and 77% of it is water then the mass of water in our brains is 1.4kg * .77 = 1.078 kg. Next we want to convert that to grams 1000g = 1 kg. 1000g * 1.078kg = 1078g. If it takes 1 calorie to heat up one gram of water we now divide how many calories our brains produce in an hour by how many grams of water our brains have. 19800 cal / 1078g = 18.37 degree C

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