Before ironing his shirt for work, Nathaniel drops some water on his iron to
test whether it is hot enough to iron his clothes. How much heat is needed to
vaporize a 5.0 � 10�4-kg drop of 20.°C water?
To calculate the amount of heat needed to vaporize the water droplet, we can use the formula:
Q = m * ΔHv
Where:
Q is the amount of heat energy required (in Joules)
m is the mass of the water droplet (in kg)
ΔHv is the latent heat of vaporization for water (in J/kg)
The latent heat of vaporization for water is the amount of heat required to convert one kilogram of water from liquid to vapor at a given temperature. For water at 100°C, the value is approximately 2.26 x 10^6 J/kg.
However, in this case, the water droplet is initially at a temperature of 20°C, which means we need to take into account the additional heat required to raise its temperature to the boiling point (100°C). This can be calculated using the specific heat capacity of water, which is approximately 4.18 x 10^3 J/(kg·°C).
Let's break down the calculation step by step:
Step 1: Calculate the heat required to raise the temperature of the water droplet from 20°C to 100°C.
Q1 = m * C * ΔT
Where:
C is the specific heat capacity of water (in J/(kg·°C))
ΔT is the change in temperature (100°C - 20°C)
Step 2: Calculate the heat required to vaporize the water droplet at 100°C.
Q2 = m * ΔHv
Finally, we can add up the two amounts of heat to get the total heat required:
Q = Q1 + Q2
Let's plug in the values and calculate:
Step 1:
Q1 = (5.0 x 10^-4 kg) * (4.18 x 10^3 J/(kg·°C)) * (100°C - 20°C)
Step 2:
Q2 = (5.0 x 10^-4 kg) * (2.26 x 10^6 J/kg)
Q = Q1 + Q2
Now, you can perform the calculations to find the total amount of heat required to vaporize the water droplet.