Susan, whose mass is 57 kg , climbs 52 m to the top of the Cape Hatteras lighthouse.
When exercising, the body must perspire and use other mechanisms to cool itself to avoid potentially dangerous increases on body temperature. If we assume that Susan doesn't perspire or otherwise cool herself and that all of the "lost" energy goes into increasing her body temperature, by how much would her body temperature increase during this climb?
**Note** In part A I calculated her increase in potential energy to be 29000 J using m*g*deltay. In part B I calculated her typical efficiency at 25% to be 120000 J. I am unsure if you will need these two values in the final calculation described above.
Thank you in advance for any help you can offer :)
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Your numbers don't add up. 29000 J is correct. You didn't provide the information to calculate efficiency, but assuming it's 25%, then 29000 J is 25% of the energy she generated, so she generate 4 x 29000 which would be 116000 Joules. Were you rounding to two significant figures? That would be OK.
Anyway, the difference between what she generated (116 kJ or 120 kJ) and what was used (29 kJ) is the lost energy. Set that equal to m * c * delta-T where m = her mass, c = her specific heat and delta-T = change in temperature. Solve for delta-T.
Edit: Since people are mostly water, the standard approximation is to use the specific heat of water, c = 4.19 J/gm-C = 4190 J/kg-C
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