A pot containing 1.09 liter of water, initially at 18°C, is placed on a 1101 W electric heating element.
(a) How much heat must be supplied to the water to bring it to a boil?
(b) How much heat is necessary to boil all the water away?
What is the minimum time required to boil all the water away?
L = 2260000 J/kg is the heat of vaporization,
ρ =1000 kg/m^3 is the density of the water,
c = 4185.5 J/(kg•K) is heat capacity of water.
Q1 = c•m•ΔT= c•m•ΔT = c•ρ•V •ΔT = =4180•1000•1.09•10^-3•82 = 3.73•10^5 J
Q2 = L•m = L• ρ•V =2260000 • 1000•1.09•10^-3 =2.46•10^6 J
Q = Q1+Q2 = P•t,
t = (Q1+Q2)/P =
= 3.73•10^5+2.46•10^6)/ 1101= 2574 s = =42.89 min.
To answer these questions, we need to understand the concepts of specific heat capacity and latent heat.
(a) To calculate the amount of heat required to bring the water to a boil, we need to consider two steps:
Step 1: Heating the water from its initial temperature to the boiling point.
Step 2: Heating the water from the boiling point to when it starts boiling.
Here's how we can calculate the heat required for each step:
Step 1:
First, we need to calculate the temperature difference (∆T) between the initial temperature (18°C) and the boiling point of water (100°C):
∆T = 100°C - 18°C = 82°C
Next, we need to calculate the heat required to raise the temperature of the water. The specific heat capacity (c) of water is approximately 4.18 J/g°C:
q1 = m * c * ∆T
where:
q1 = heat required for Step 1
m = mass of water
c = specific heat capacity of water
∆T = temperature difference
The mass of water can be determined using its density (approximately 1 g/mL or 1 kg/L) and volume (1.09 L):
m = density * volume
Finally, we can calculate the heat required for Step 1.
Step 2:
The heat required to bring the water to its boiling point (at 100°C) without boiling is calculated using the following equation:
q2 = m * Latent Heat of Vaporization
where:
q2 = heat required for Step 2
m = mass of water
Latent Heat of Vaporization = 2260 J/g
Now, we can calculate the total heat required to bring the water to a boil:
Total heat = q1 + q2
(b) To calculate the heat necessary to boil all the water away, we need to consider the latent heat of vaporization only. Since boiling the water will convert it into steam, we can calculate the heat using the equation:
Total heat = m * Latent Heat of Vaporization
where:
m = mass of water
Latent Heat of Vaporization = 2260 J/g
To find the mass of the water, we use the given volume and density as mentioned in part (a).
Now that we know the total heat required, we can move on to the minimum time required to boil all the water away.
(c) To calculate the minimum time required, we need the power (P) of the heating element, which is given as 1101 W. The relationship between power, heat, and time is:
Power = Heat / Time
Rearranging the equation, we get:
Time = Heat / Power
By substituting the respective values for heat (from part (b)) and power, we can calculate the minimum time required to boil all the water away.