During strenuous work a human body generates about 2,400 btus of body heat per hour. if 7 bodybuilders are in a gym that is 20 ft × 25 ft × 12 ft lifting weights, how many btus per cubic foot do they produce in 3 hours? (to the nearest tenth) a) 2.8 btus/ft3 b) 8.4 btus/ft3 c) 33.7 btus/ft3 d) 100.8 btus/ft3

By doing dimensional analysis, we can easily calculate for what is being asked here. We do as follows:

Given:
Energy per time = 2400 BTU/hr
time period = 3 hrs
number of subjects = 7
Measurement of the weights = 20 ft × 25 ft × 12 ft

The energy produced for 3 hours would be:

2400 BTU/hr ( 3hr) = 7200 BTU
Volume of each weight = 20 ft × 25 ft × 12 ft = 6000 ft^3

Energy per volume = 7200 / 6000 = 1.2 BTU/ft^3

However, we have 7 bodybuilders producing this amount therefore,

Total energy produced = 7 (1.2 BTU/ft^3) = 8.4 BTU/ft^3