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.

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 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.

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.

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, C_s = 2.06 J/(g °C), or liquid water, C_l = 4.184 J/(g °C), or vapor, C_v = 2.01 J/(g °C).

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

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, ΔH_f, or is the heat of vaporization for liquid water, ΔH_v, 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.

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.

For more practice, please reference the flashcards associated with this article!