An inventor develops a stationary cycling device by which an individual,while pedaling,can convert all of the energy expended into heat for warming water.What minimum power must be generated if 210 g water (enough for 1 cup of coffee)is to be heated in 14.0 min from 26.0°C to 84.0°C? (1 cal = 4.186 J,the specific heat of water is 4 186 J/kg⋅°C)
A)3 640 W
B)289 W
C)60.7 W
D)850 W
E)42.5 W

Question

Quizplus · Accepted Answer

To find the minimum power, first calculate the energy required to heat the water using the formula: Q = mcΔT. Here, m = 0.210 kg, c = 4186 J/kg°C, and ΔT = 84.0°C - 26.0°C = 58.0°C. So, Q = 0.210 kg * 4186 J/kg°C * 58.0°C = 50,946.12 J. The time is 14.0 min = 840 s. Power is energy divided by time: P = Q/t = 50,946.12 J / 840 s ≈ 60.7 W.

An Inventor Develops a Stationary Cycling Device by Which an Individual,while