240 grams of cold water are heated up in a microwave with a power output of 1,000 watts. It takes the glass exactly 16 minutes to turn all of that water into steam.

Question

a) Find the amount of energy involved in this entire process, in J.

b) Find the amount of energy involved only in evaporating the water when it is at 100 °C, in J.

c) Find the amount of energy involved only in raising the water's temperature to its boiling point, in J.

d) Find the water's initial temperature, in °C.

Answer 1

Let's looks at what's given:

m = 240 grams = 0.24 kg

The substance is liquid water

Power = 1000 Watts

Time = 16 minutes = 960 seconds

a) We're given the Power, which is defined as the change in energy over time. We have the time as well, so we can use the definition of Power to find that energy:

P = ΔE/Δt

ΔE = P · Δt = 1000 W · 960 s = 960,000 J

b) The energy required for a phase change is equal to the mass of the substance times the latent heat for that particular transformation (Q = mL). Here, we want the latent heat of vaporization for water, since we want the liquid-gas transformation. A quick internet search gives the value of L = 2,264,000 J/kg

Q = mL = 0.24 kg · 2,264,000 J/kg = 543,360 J

c) The energy for that temperature change is the total energy we found in (a) minus the energy for the phase change found in (b)

Q = 960,000 J - 543,360 J = 416,640 J

d) The energy for a change in temperature is equal to the mass of the substance times the specific heat capacity of the material and its phase times the change in temperature: Q = mCΔT. A quick internet search gives the specific heat capacity of liquid water to be 4182 J/kg °C. Solving for the change in temperature, we have:

Q = mCΔT

ΔT = Q / (mC) = 416,640 J / (0.24 kg · 4182 J/kg °C) = 415 °C

Since the final temperature is 100 °C, this means that the initial temperature :

ΔT = T_F - T₀

T₀ = T_F - ΔT = 100 °C - 415 °C = -315 °C

This is obviously a big problem! In reality, that 240 grams would have to start as solid ice, and we would have to include (1) the energy for a temperature change from 100 °C down to the freezing point of 0 °C, (2) the energy for a phase change from a liquid to a solid (fusion), and (3) the temperature change as a solid from 0 °C down to the unknown initial temperature