# Heating Curve for Water

Water isn’t called our life’s medium for no reason. Without water, we simply can’t sustain life. It is water that facilitates cellular processes, vital chemical reactions, and basically the function of our whole planet. This is why studying the energy changes due to heating or cooling water is important for us to understand.

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So, without further ado, let's talk about the heating curve for water!

• First, we’ll go over what the heating curve of water is.

• Next, we’ll look at the meaning of a heating curve and a basic graph for the heating curve of water.

• Thereafter, we’ll view the heating curve for the water equation.

• Finally, we’ll learn to calculate energy changes for the heating curve of water.

## Heating Curve of Water Meaning

For starters, let's look at the meaning of the heating curve of water.

The heating curve for water is used to show how the temperature of a certain amount of water changes as heat is added constantly.

The heating curve for water is important as it shows the relationship between the amount of heat put in and the temperature change of the substance.

In this case, the substance is water.

It’s vital for us to comprehend the phase changes of water, which can conveniently be graphed into a chart, as they display characteristics that are common when water is involved.

For instance, it’s useful to know at what temperature ice melts or at what temperature water boils when you want to cook daily.

Figure 1: To boil a cup of tea we need the heating curve for water. Daniela Lin, Study Smarter Originals.

Even to brew a cup of tea like the one shown above, you need to boil water. Knowing the temperature at which water boils is important for this process. This is where a graphical representation of the heating curve for water is helpful.

### Graphing a Heating Curve for Water

To graph a heating curve for water, we first need to consider the definition of the heating curve of water that we mentioned earlier.

This means that we want our graph to reflect temperature changes for water when we add a certain amount of heat.

Figure 2: Heating Curve for Water shown. Daniela Lin, Study Smarter Originals.

Our x-axis measures the amount of heat added. Meanwhile, our y-axis deals with the temperature changes of water as a result of us adding an certain amount of heat.

After understanding how we graph our x and y-axis, we also need to learn about the phase changes.

In the figure below, our water starts out as ice at around -30 degrees Celsius (°C). We begin by adding heat at a constant rate. Once our temperature reaches 0 °C, our ice enters the melting process. During the phase changes, the temperature of the water remains constant. This is denoted by the horizontal dotted line shown in our graph. This occurs because as we add the heat to the system it does not change the temperature of the ice/water mixture. Note, that heat and temperature are not the same things from a scientific standpoint.

The same thing happens later on when our now liquid water starts to boil at a temperature of 100 °C. As we add more heat to the system we get a water/vapor mixture. In other words, the temperature stays at 100 °C until the added heat overcomes the attractive forces of hydrogen bonding in the system and all the liquid water becomes vapor. After that, the continued heating of our water vapor leads to an increase in temperature.

For a clearer understanding, let’s go over the graphical representation of the heating curve of water again, but this time with numbers detailing the changes.

Figure 3: Graphical representation of heating curve for water, with the phases, labeled. Daniela Lin, Study Smarter Originals.

From figure 3 we can see that:

1) We start out at -30 °C with solid ice and standard pressure (1 atm).

1-2) Next, from steps 1-2, as the solid ice heats up the water molecules begin to vibrate as they absorb kinetic energy.

2-3)Then from steps 2-3, a phase change occurs as the ice starts to melt at 0 °C. The temperature remains the same, as the constant heat being added is helping overcome attractive forces between the solid water molecules.

3) At point 3, ice has successfully melted into water.

3-4) This means from steps 3-4, as we keep adding constant heat, the liquid water starts heating up.

4-5)Then steps 4-5, involve another phase change as liquid water starts to vaporize.

5) Finally, when the attractive forces between the liquid water molecules are overcome, water becomes steam or gas at 100 °C. The continued heating of our steam is what causes the temperature to keep rising beyond 100 °C.

For more information regarding attractive forces please reference our “Intermolecular Forces” or “Types of Intermolecular Forces” article.

## Heating Curve of Water Examples

Now that we understand how to graph the heating curve for water. Next, we should concern ourselves with real-world examples of how to use the heating curve of water.

### Heating Curve of Water Equation and Experiment

Part of understanding how to use the heating curve of water is to understand the equations involved.

The slope of the line in our heating curve depends on the mass and specific heat of the substance we are dealing with.

For example, if we’re dealing with solid ice, then we need to know the mass and specific heat of ice.

The specific heat of a substance (C) is the number of joules required to raise 1g of a substance by 1 Celsius.

Figure 4: Graphical representation of heating curve for water, with a number of heat formulas, labeled for clarity. An explanation of each change is provided below. Daniela Lin, Study Smarter Originals.

Temperature changes occur when the slope isn’t a constant line. This means they occur from steps 1-2, 3-4, and 5-6.

The equations we use to calculate these specific steps are:

Heat Curve of Water Equation

$$Q= m \times C \times \Delta T$$

where,

• m= mass of a specific substance in grams (g)

• C= specific heat of capacity for a substance (J/(g °C))

• The specific heat capacity, C, is also different depending on whether it is ice, Cs = 2.06 J/(g °C), or liquid water, Cl = 4.184 J/(g °C), or vapor, Cv = 2.01 J/(g °C).

• $$\Delta T$$ = change in temperature (Kelvin or Celsius)

This equation is for the temperature change parts of the graph as a function of the energy. Since there are temperature changes at these stages, our equation to find the heat changes of water at these specific points involves the mass, specific heat of capacity, and change in temperature of the substance we’re dealing with.

Note, that Q stands for the amount of heat transferred to and from an object.

In contrast, phase changes occur when the slope is zero. Which means they occur from steps 2-3 and 4-5. At these changes in phase, there’s no temperature change, our equation only involves the mass of a substance and the specific heat of change.

For steps 2-3, since there’s no change in temperature, we’re adding heat to help overcome the hydrogen bonding within the ice to turn it into liquid water. Then our equation only deals with the mass of our specific substance, which is ice at this point of the calculation, and the heat of fusion or enthalpy change (H) of fusion.

This is because the heat of fusion deals with the change in heat due to energy being provided in the form of constant heat to liquefy ice.

Meanwhile, steps 4-5 it’s the same as steps 2-3 except we’re dealing with the change in heat due to the vaporization of water to steam or enthalpy of vaporization.

Heat Curve of Water Equation

$$Q = n \times \Delta H$$

where,

• n = number of moles of a substance

• $$\Delta H$$ = change in heat or molar enthalpy (J/g)

This equation is for the phase change parts of the graph, where ΔH is either the heat of fusion for ice, ΔHf, or is the heat of vaporization for liquid water, ΔHv, depending on the which phase change that we are calculating.

### Calculating Energy Changes for the Heating Curve of Water

Now that we’ve gone over the equations relating to all the changes in our heating curve for water. We will calculate energy changes for the heating curve of water by using the equations we learned above.

Using the given information below. Calculate the energy changes for all the steps shown in the heat curve for the water graph up to 150 °C.

Given a mass (m) of 90 g of ice and the specific heats for ice or Cs = 2.06 J/(g °C), liquid water or Cl = 4.184 J/(g °C), and vapor or Cv = 2.01 J/(g °C). Find all the quantity of heat (Q) needed if we convert 10 g of ice at -30 °C to vapor at 150 °C. You will also need the enthalpy values of fusion, ΔHf = 6.02 kJ/mol, and enthalpy of vaporization, ΔHv = 40.6 kJ/mol.

The solution is:

Figure 5: Graphical representation of the heating curve of water labeled for example. Daniela Lin, Study Smarter Originals.

1-2) Ice being heated: It's a temperature change as the slope isn't a flat horizontal line.

$$Q_1 = m \times C_s \times \Delta T$$

$$Q_1$$ = (90 g of ice) x (2.06 J/(g °C)) x (0 °C-(-30°C ))

$$Q_1$$ = 5,562 J or 5.562 kJ

2-3) Ice being melted (melting point of ice): It's a phase change as the slope is zero at this point.

$$Q_2 = n \times \Delta H_f$$

We need to convert grams to moles given 1 mol of water = 18.015 g of water.

$$Q_2$$ = (90 g of ice) x $$\frac {1 mol} {18.015 g}$$ x 6.02 kJ/mol

$$Q_2$$ = 30.07 kJ

3-4) Liquid water being heated: It's a temperature change as the slope isn't a flat horizontal line.

$$Q_3 = m \times C_l \times \Delta T$$

$$Q_1$$ = (90 g of ice) x (4.184 J/(g °C)) x (100 °C-0°C )

$$Q_1$$ = 37,656 J or 37.656 kJ

4-5) Water being vaporized (boiling point of water): It's a phase change as the slope is zero.

$$Q_4 = n \times \Delta H_v$$

We need to convert grams to moles given 1 mol of water = 18.015 g of water.

$$Q_2$$ = (90 g of ice) x $$\frac {1 mol} {18.015 g}$$ x 40.6 kJ/mol = 202.83 kJ

5-6) Vapor being heated: It's a temperature change as the slope isn't a flat horizontal line.

$$Q_5 = m \times C_v \times \Delta T$$

$$Q_1$$ = (90 g of ice) x ( 2.01 J/(g °C)) x (150 °C-100°C)

$$Q_1$$ = 9,045 J or 9.045 kJ

Thus, the total amount of heat is all of the Q values added up

Q total = $$Q_1 + Q_2 + Q_3 + Q_4 + Q_5$$

Q total = 5.562 kJ + 30.07 kJ + 37.656 kJ + 202.83 kJ + 9.045 kJ

Q total = 285.163 kJ

The quantity of heat (Q) needed if we convert 10 g of ice at -30 °C to vapor at 150 °C is 285.163 kJ.

You’ve reached the end of this article. By now you should understand, how to construct a heating curve for water, why it's important to know the heating curve for water, and how to calculate the energy changes associated with it.

## Heating Curve for Water - Key takeaways

• The heating curve of water is used to show how the temperature of a certain amount of water changes as heat is added constantly.

• The heating curve for water is important as it shows the relationship between the amount of heat put in and the temperature change of the substance.

• It’s vital for us to comprehend the phase changes of water, which can conveniently be graphed into a chart.

• The slope of the line in our heating curve depends on the mass, specific heat, and phase of the substance we are dealing with.

## References

1. Libretexts. (2020, August 25). 11.7: Heating curve for water. Chemistry LibreTexts.
2. The physics classroom tutorial. The Physics Classroom. (n.d.).
3. Libretexts. (2021, February 28). 8.1: Heating curves and phase changes. Chemistry LibreTexts.

#### Flashcards in Heating Curve for Water 9

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What does the slope of the heating curve for water represent?

The slope of the heating curve for water represents the rising temperature and phase changes in water as we add a constant rate of heat.

What is the heating curve of water?

The heating curve of water is used to show how the temperature of a certain amount of water changes as heat is added constantly.

What is the aim of heating and cooling curve of water?

The aim of heating curve of water is to show how the temperature of a known amount of water changes as constant heat is added. In contrast, the cooling curve of water is to show the temperature of a known amount of water changes as constant heat is released.

How do you calculate heating curve?

You can calculate the heating curve by using the quantity of heat equation (Q) = m x C x T for the temperature changes and Q= m x H for phase changes.

What is the heating curve diagram?

The heating curve for the water diagram shows the graphical relationship between the amount of heat put in and the temperature change of the substance.

## Test your knowledge with multiple choice flashcards

Why is the heating curve of water important?

What happens during a phase change for the heating curve for water?

What does the slope of the line in our heating curve for water depend on?

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