16. The heat required to convert 2 kg of water at 20°C in a calorimeter to steam at 100°C and at atmospheric pressure (1 atm) is ______ kJ.
(Specific heat capacity of water = 4.2 kJ kg⁻¹ K⁻¹ and latent heat of steam = 2256 kJ kg⁻¹)
Heat Required to Convert 2 kg of Water at 20°C into Steam at 100°C
Correct Answer: 5184 kJ
Understanding the Heat Required to Convert Water into Steam
This problem involves two separate stages of heat transfer. The water initially has a temperature of 20°C, but the final state required is steam at 100°C. Therefore, the entire transformation cannot be calculated using only one heat formula.
In the first stage, heat must be supplied to increase the temperature of the water from 20°C to its boiling point of 100°C. This heat is called sensible heat because it causes a measurable change in temperature without changing the physical state of the water.
In the second stage, additional heat must be supplied to convert the water at 100°C into steam at 100°C. During this stage, the temperature remains constant, but the physical state changes from liquid to gas. The energy required for this phase change is calculated using the latent heat of vaporization.
Therefore, the total heat required is:
Total heat required = Heat required to raise the temperature of water + Heat required to convert water into steam
Given Values in the Question
The mass of water is:
m = 2 kg
The initial temperature of water is:
Ti = 20°C
The final temperature at which water boils and changes into steam is:
Tf = 100°C
The specific heat capacity of water is:
c = 4.2 kJ kg−1 K−1
The latent heat of steam, or latent heat of vaporization of water, is:
L = 2256 kJ kg−1
Step-by-Step Calculation of the Total Heat Required
Step 1: Calculate the Temperature Increase of Water
The water must first be heated from 20°C to 100°C. Therefore, the change in temperature is:
ΔT = Tf − Ti
ΔT = 100 − 20
ΔT = 80 K
A temperature difference has the same numerical value in degrees Celsius and kelvin. Therefore, a temperature rise of 80°C is equivalent to a temperature rise of 80 K.
Step 2: Calculate the Heat Required to Raise the Temperature of Water
The heat required to increase the temperature of a substance without changing its physical state is calculated using:
Q1 = mcΔT
Substituting the given values:
Q1 = 2 × 4.2 × 80
Q1 = 672 kJ
Therefore, 672 kJ of heat is required to raise the temperature of 2 kg of water from 20°C to 100°C.
Step 3: Calculate the Heat Required to Convert Water into Steam
Once the water reaches 100°C, it must be converted into steam at the same temperature. During this phase change, the temperature does not increase. The supplied heat is used to overcome the intermolecular forces between water molecules and transform the liquid into vapour.
The heat required for vaporization is calculated using:
Q2 = mL
Substituting the given values:
Q2 = 2 × 2256
Q2 = 4512 kJ
Therefore, 4512 kJ of heat is required to convert 2 kg of water at 100°C completely into steam at 100°C.
Step 4: Calculate the Total Heat Required
The total heat required is the sum of the heat used to raise the temperature of the water and the heat used for vaporization:
Q = Q1 + Q2
Substituting the calculated values:
Q = 672 + 4512
Q = 5184 kJ
Why Are Two Different Heat Calculations Required?
The transformation from water at 20°C to steam at 100°C includes both a temperature change and a change of state. These are two physically different processes, so they require different equations.
From 20°C to 100°C, the water remains in the liquid state and its temperature increases. Therefore, the heat is calculated using Q = mcΔT. At 100°C and atmospheric pressure, the water begins to boil. During boiling, the temperature remains constant while liquid water changes into steam, so the heat required is calculated using Q = mL.
Adding these two quantities gives the complete energy required for the entire process.
Role of Atmospheric Pressure in the Question
The atmospheric pressure of 1 atm is important because the boiling point of water depends on pressure. At standard atmospheric pressure, water boils at 100°C. Therefore, once the water reaches 100°C at 1 atm, any additional heat supplied is used for the phase transition from liquid water to steam rather than for further increasing the temperature.
Final Answer
The total heat required to convert 2 kg of water at 20°C into steam at 100°C and 1 atm pressure is 5184 kJ.
The calculation includes 672 kJ to heat the water from 20°C to 100°C and 4512 kJ to convert the water at its boiling point into steam. Therefore:
Total heat required = 672 + 4512 = 5184 kJ
