Question

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 300 g water (enough for 1 cup of coffee) is to be heated in 10 min from 20°C to 95°C?
(1 cal = 4.186 J, the specific heat of water is 4 186 J/kg⋅°C)
a. 9 400 W
b. 590 W
c. 160 W
d. 31 W

Answer 1

Answer:

c. 160 W

Explanation:

The energy needed to increase the temperature of a certain substance is given by:

$Q=mC\Delta T$

In this case, Q is the heat for warming the water, m the mass of the water, C the specific heat of water and $\Delta T$ the temperature change.

$Q=(3*10^{-3}kg)(4186\frac{J}{kg\cdot ^\circ C})(75^\circ C)\\Q=9.42*10^{4}J$

one watt minute is equivalent to 1 watt (1 W) of power sustained for 1 minute. One watt is equal to 1 J/s. So, one watt minute is equal to 60 J. So, in ten minutes we have 600J:

$Q=9.42*10^{4}J*\frac{1Wmin}{60J}*\frac{1}{10min}\\Q=157W$