Question

Count Rumford used a horse to turn cannon boring machinery. He showed that a single horse could heat 11.6 kg of ice water (T=273K) to T=355K in 2.5 hours. Assuming the same rate of work, how high could a horse raise a 193 kg weight in 3.0 minutes? Assume the heat capacity of water is 4.18 J⋅K−1⋅g−1.

Answer 1

Heat absorbed by ice

= heat absorbed for phase change + heat absorbed to increase the temperature

= mass x heat of fusion + mass x Cp x (T2-T1)

= 11.6 kg x 334000 J/kg + 11.6 kg x 4180 J/kg-K x (355 - 273)K

= 3874400 + 3976016

= 7850416 J

Rate of heat absorbed = 7850416 J / (2.5 hr x 3600s/hr)

= 872.268 J/s

Rate of work = m x g x h / time

872.268 J/s = 193 kg x 9.81 m/s2 x h / (3 min x 60s/min)

h = 80.93 m

80.93 m high could a horse raise a 193 kg weight in 3.0 minutes?