Question

Many people believe the perfect recipe for brewing a cup of green tea is to steep the tea in 180°F water. How much heat energy (kJ) must be supplied to bring a cup of water (about 240 mL) from room temperature to the ideal steeping temperature for green tea? Express your answer to two decimal places.



A microwave with a rating of 1100 Watts means that it generates 1100 Joules of energy per second. If all the energy produced by a 1100 Watt microwave ended up as heat transferred into the cup of water used to make the green tea, how many seconds would it take to heat the water to the desired temperature for brewing the tea? Do not work from your rounded answer above. Express your answer to two decimal places.

Answer 1

(A.) heat energy to be supplied = 57.46 kJ

(B.) time taken to heat the water = 52.24 s

Explanation

(A.) volume of water = 240 mL

mass of water = (volume of water) * (density of water)

mass of water = (240 mL) * (1.00 g/mL)

mass of water = 240 g

initial temperature of water = room temperature = 25 ^oC

final temperature = 180 ^oF

final temperature = (180 - 32) * (5/9)

final temperature = 82.2 ^oC

energy required = (mass of water) * (specific heat of water) * (final temperature - initial temperature)

energy required = (240 g) * (4.184 J/g.^oC) * (82.2 ^oC - 25 ^oC)

energy required = 57460.3 J

energy required = 57.46 kJ

(B.) time required to heat = (energy required) / (power)

time required to heat = (57460.3 J) / (1100 J/s)

time required to heat = 52.24 s