A small electric immersion heater is used to heat 100 g of water for a cup of instant coffee. The heater is labeled "200 watts" (it converts electrical energy to thermal energy at this rate). Calculate the time required to bring all this water from 23.0 0C to 100 0C, ignoring any heat losses.
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200W means the heater adds 200Joules of energy to the water each second
the amount of energy needed to heat 100g of water from 23C to 100 C is given by:
Q=mc(delta T) where m is the mass of the water, c is the specific heat, and delta T is the change of temp
here, m=100 g
c=4.2 J/gram/deg C
delta T= 77
thus, Q=100 g x 4.2 J/g/C x 77C = 32.3 KJ
if the heater provides 200J/s, then the time needed to heat the water is
t=32.3kJ/200J/s = 161.7 s
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