Science Facts

What Is Latent Heat? – Types, Formula, Problem & Example

Latent Heat

This lecture will provide an overview of latent heat and look at how we can use physical property data to help us with latent heat calculations. So the term latent heat is used to describe heat transfer. It is associated with a phase change, and specifically a phase change at constant temperature and pressure. So by considering the phases, the only variable is changing latent heat from sensible heat. It is the heat transfer associated with the temperature change.

The phase changes in chemical engineering operations are the transition between the solid and a liquid and liquid and vapor. The transition of a solid to a liquid is melting. And the change in specific enthalpy associated with that change is the heat of melting. The transition between a liquid and vapor is vaporization, and the specific enthalpy change associated with that process is the heat of vaporization.

What is latent heat?

The latent heat is the energy required to change the substance’s state from one phase to another. In other words, it’s the amount of energy to make a certain amount. And it’s the phase of a substance to go from a liquid to a gas or a solid to a liquid and so forth. Different substances will have different values for their latent heat. The term latent heat was invented by Joseph Black in 1750 in search of ideal quantities of fuel and water for their distilling process.

Latent heat graph
Latent heat graph

What is the temperature change that happens when you add heat to ice or water? When someone adds heat to the ice, the ice will melt, and then the water with the temperature rise, and it will continue for some time. Look at the temperature vs. time graph where the X-axis represents the time, and Y-axis represents temperature. After some time, the temperature rise stops, so it goes on rising for a specific time. Then it becomes flat for some time. It remains flat at 100 degrees Celsius.

What’s happening here? It’s the latent heat of vaporization. The water is turning into water vapor into gas or steam. So the water the liquid is changing into the gas at 100 degrees centigrade. When the change of state is happening from liquid to gas, there is no change of temperature.

Phase i – Phase transition solid to liquid. Latent heat of fusion is needed to break the solid bond.

Phase ii – Phase transition liquid to gas. Latent heat of vaporization is needed to break liquid bonds.

To understand the topic of latent heat, you should be familiar with:

  • The law of conservation of energy.
  • The effect of intermolecular forces on phase transitions.

Types of latent heat: There are three different types of latent heat. They are,

  • Latent Heat of Fusion.
  • Latent Heat of Vaporization.
  • Latent Heat of Sublimation.

Latent heat formula: Two formulas depending on the phase or temperature for calculating latent heat or energy.

E = m × L ( For phase change).
Q = m × c × ΔT ( For temperature change ).

Here, E & Q is the energy for a state change, and m (kg) is mass. L is the specific latent heat (J/kg) & c is the specific heat capacity.

Latent heat problem & solution

Problem: How much energy is needed to take 2.5 kilograms of ice (solid water) at -15 °C and turn it into liquid water at 35 °C?

Solution: The first one is the energy needed to raise the temperature from minus 15 to zero. That’s when it’s going to be solid.

Here, ΔQ = 2.5 kg, c = 2100 J/kg °C, ΔT = 15 °C.

ΔQ (ice) = m × c × ΔT = 2.5 kg × 2100 J/kg °C × 15 °C = 78,750 J.
ΔQ (melting) = m × L = 2.5 kg × (333.10 × 1000) = 832,500 J.
ΔQ (liquid) = m × c × ΔT = 2.5 kg × 4186 J/kg °C × 35 °C = 366,275 J.

ΔQ (total) = ΔQ (ice) + ΔQ (melting) + ΔQ (liquid) = 1198,854 J.

Sensible heat: Sensible heat is a sensing heat that increases matter and can be sensed. Suppose you feel something warm that is sensible heat.

Reasonable heat: Latent heat is frequently called reasonable heat. It reflects heat move among issues and its environment.

Latent heat of fusion

Latent heat of fusion of ice is the amount of heat required to change a unit mass of ice at its melting point into liquid at the same temperature. Did you know that the latent heat of fusion affects our lives to a great extent? Let discuss some of the consequences of latent heat of fusion of ice. The temperature becomes very low after a hailstorm.

It is because every kilogram of ice absorbs 336 kilojoules of heat energy from the surroundings and melts. As a result, the weather becomes very cold. For the same reason, it becomes bitterly cold as soon as the snow starts melting in cold countries.

The weather gets pleasant when freezing starts in cold countries. Every kilogram of water on freezing releases 336 kilojoules of heat. Thus when freezing starts in cold countries, a huge amount of heat energy is released into the atmosphere. And this makes the weather pleasant.

Snow on the mountains does not melt all at once. Ice or snow has a very high latent heat of fusion equal to 336 kilojoules per kilogram. To melt 1 kg of ice or snow on mountains, the required heat energy must be absorbed from the Sun. Therefore snow on the mountains changes into the water slowly as it absorbs heat from the Sun.

Water in lakes and ponds in cold countries does not freeze all at once. The water freezes slowly and thus saves the surroundings from freezing and makes that atmosphere moderate. Aquatic life can survive in cold countries even if the atmosphere’s temperature is zero degrees Celsius or below zero degrees Celsius.

This is because the water does not start freezing immediately. The water on the surface will freeze first when the temperature goes below zero degrees Celsius. But below the surface, it is not frozen. The high latent heat of fusion of ice and the anomalous water expansion enables aquatic life to survive in cold countries.

Anomalous water expansion: When water at zero degrees Celsius is heated, it contracts to four degrees Celsius instead of expanding and behaves like any other liquid about four degrees Celsius. This behavior of water is referred to the as anomalous expansion of water.

The natural consequence of the anomalous expansion of water: When the water on the surface of a water body cools down to four degrees Celsius, its density increases and sinks. The warmer layer of water from the bottom rises to the surface. This layer cools to zero Degree Celcius and thus forming a layer of ice.

The dense layer of water at four degrees Celsius remains in the liquid state. The ice formed on the surface is a bad conductor of heat and provides a suitable condition for fish and other aquatic animals’ survival.

Latent heat of vaporization

Latent heat of vaporization or latent heat of sublimation tells how much energy is needed to go from a solid to a liquid. And likewise, how much energy will be released if convert the liquid back into a solid. The hydrogen bonds between the water molecules must be broken for water to change from a liquid to a gas.

To convert water into a gas form, hydrogen bonds must be detached from each other. It needs to break these hydrogen bonds, and the hydrogen bonds barely exist in the gas form. Hydrogen bonds are much stronger than most other types of intermolecular forces. A relatively high amount of energy must be used to break them. So again, the energy used to pull water molecules apart is provided with heat energy. And the amounts are much more relative to other types of molecules.

Water has a high latent heat of vaporization. Vaporization means two things. It means turning a liquid into a gas, but this can be done in two methods.

  • By evaporation.
  • By boiling.

They both come under the heading of vaporization because it’s becoming vapor. So latent heat of vaporization is the amount of energy needed to vaporize one gram of a substance. For example, To change one gram of liquid water into vapor, the energy is the latent heat of vaporization. It is different from specific heat capacity, which is about raising the water temperature by one degree.

When the water does evaporate and those hydrogen bonds are broken, the water molecules that can break their hydrogen bonds have the highest kinetic energy. Because that heat energy has been input. The energy will break certain bonds that did exist as that energy is transferred to the bonds.

And then those water molecules are free to become a gas. So the ones that can do this have the highest kinetic energy. The ones staying put and bonded to other molecules in a liquid form have lower kinetic energy.

When the ones with the highest energy become gas and they’ve escaped, there’s a decrease in the remaining water molecules’ average kinetic energy. Imagine that several molecules are being released because several hydrogen bonds have been broken. The average energy in the whole area has now gone down. The kinetic energy has gone down, and kinetic energy means temperature. The temperature of the water has now decreased.

So evaporation as a process has a cooling effect whereby those specific water molecules evaporate. The rest of everything left behind has reduced its temperature. It is an excellent physiological mechanism for sweating. Humans use the evaporation of sweat from our skin as an effective way of reducing our body temperature. So if the temperature around us rises, we need to be aware of this because our proteins can denature if it goes too high.

What is specific latent heat?

The specific latent heat of a substance is the amount of energy required to change the state of one kilogram of substance with no change in temperature. For melting 1 kilogram of ice, how much energy would that take? Scientists have worked this out, and it takes 334,000 joules of energy to melt 1 kilogram of ice. Scientists call this energy the specific latent heat of fusion. So this is the energy required to change 1 kilogram of a substance from a solid to a liquid with no temperature change.

How much energy would that take to change a substance from a liquid to a gas or boil it? Scientists call this the specific latent heat of vaporization. The specific latent heat of vaporization is the energy required to change one kilogram of a substance from a liquid to vapor with no temperature change.

Specific latent heat formula

It states that a state change’s energy equals the multiplication of mass and specific latent heat.

E = m × L ( For phase change).
Q = m × c × ΔT ( For temperature change ).

Here, E (J) is the energy for a state change, and m (kg) is mass. L is the specific latent heat (J/kg) & c is the specific heat capacity.

  • Specific heat of water is 4,200 J/kg °C.
  • Specific heat of ice is 2093 J/kg °C.
  • Specific heat of steam is 2.010 kJ °C kg-1.

Specific latent heat problem & solution

Problem 1: Calculate the energy required to convert 0.5kg of ice to liquid water. The specific latent heat of fusion of water is 334000 J/kg.

Solution: The energy for a change of state equals the mass multiplied by the specific latent heat.

In this case,

m = 0.5 kg.
L = 334000 J/kg.

Energy required, E = m × L = 0.5 kg × 334000 J/kg = 167,000 J.

Problem 2: Calculate the energy required to convert 0.15kg of ethanol from a liquid to a vapor. The specific latent heat of vaporization of ethanol is 846,000 J/kg.

Solution: The energy for a change of state is the mass multiplied by the specific latent heat.

In this case,

m = 0.15kg.
L = 846,000 J/kg.

Energy required, E = m × L = 0.15 kg × 846,000 J/kg = 126,900 J.

Experiment of latent heat

We have a container of water to which we are adding table salt. Let’s stir that up. Next, we are going to crush up some ice to add to the saltwater. Our goal is to lower the temperature of the ice bath. Let’s add some more salt. Freezing point depression, yeah! Alright, minus 8 degrees Celcius. That’s pretty good.

Let’s place a smaller container of liquid water into this ice bath. We’ve added green food coloring to the water so that it is easier for you to understand. After a few minutes, we’ll insert a thermometer and watch the temperature drop as the ice bath cools the water. The temperature reads about -5 degrees Celsius.

The green water is still a liquid even though the temperature is below its normal freezing point. It is called supercooling. In the next step of this demo, we will add a couple of small ice pieces to the green water. The supercooled water will crystallize rapidly with the addition of ice.

Observation: When this happens, what do you predict will happen to the temperature on the thermometer? Will it increase, decrease, or stay the same? What reasoning supports your prediction?

Be sure to keep your eye on the digital display. Now we’ll drop a couple of small pieces of ice into the container of green water. Watch what’s happening. The green water froze. There is still a little bit of liquid, but we can turn the container upside down, and you can see that the ice remains inside. So, when the liquid froze, what happened to the temperature?

The temperature went up! Is this what you predicted? How can we explain what happened? Let’s think about what happens at a molecular level when water changes phase from a liquid to a solid. In the liquid state, water molecules are moving around a lot. As it gets colder, the water molecules slow down. Generally speaking, as the water cools and solidifies, there is an increase in hydrogen bonding, the dominant intermolecular force amongst the water molecules.

With this hint, can you now explain why we observed a temperature increase when the water froze? Take a moment to think about it on your own and then discuss your idea with a classmate. As we said before, when water transitions from liquid to solid, there is an increase in the number of hydrogen bonds formed between water molecules.

Does bond formation release energy or require energy? Bond formation releases energy. So then, is the process of ice forming exothermic or endothermic? Ice formation is exothermic.

If we were to balance the system and the surroundings, we would see that the energy released by the water freezing is equivalent to the thermal energy that caused the temperature to increase. This is the Law of Conservation of Energy. Generally speaking, when a substance transitions between phases, intermolecular forces between neighboring molecules are either formed or broken. When a substance transitions from a liquid to solid, intermolecular forces, or bonds, are formed, and energy is released to the surroundings. This is called the latent heat of fusion.

When a substance transitions from a solid to a liquid, energy must overcome intermolecular forces. So this is an endothermic process. Energy is absorbed from the surroundings. This is called the latent heat of melting. The latent heat of melting is equivalent in magnitude to the latent heat of fusion but opposite in sign.

Example of latent heat

The phenomenon of latent heat is using in a variety of ways to heat and cool buildings. Using melting ice to absorb thermal energy from the surroundings saves some buildings thousands of dollars annually in cooling costs.

Consider a large office building during the middle of a hot summer day. To keep the building comfortable, the air conditioning runs at full power, requiring a lot of electricity from the utility company. The utility companies can’t quickly shut down their power plants, so nearly the same amount of electricity is produced during the night as is during the day. However, nighttime demand for electricity is very low, so utility companies sell this electricity at a lower price. This is a common practice by utility companies across the U.S.

Engineers have thought of a way to buy electricity during the night when it is very cheap, but use it during the day when they need to run the air conditioning. This strategy is called peak load shifting. Think about what you have learned so far. There are a variety of ways. How do you think they do this?

We can decrease the amount of electricity needed in the daytime to cool a building to use the energy storage capacity of ice or its latent heat of melting.

Large tanks in the Bank of America Tower’s basement in New York, such as these, store water that froze overnight using cheap electricity. The ice melts and absorbs energy from the cooling fluid running through the building’s air conditioning system during the day.

Each bank of America building tank holds approximately 1600 gallons of water, translating to roughly 570-kilowatt hours of cooling capacity. Bank of America reports that these ice tanks supply 25% of their cooling energy annually.

The desire to harness latent heat has led to the developing of a class of materials called phase change materials. These materials have been specifically designed to change phase at desirable temperatures to store and release helpful energy to consumers. This slide shows some examples of these materials. This slide’s materials fall into three classes of phase change materials: inorganic salt hydrates, paraffinic hydrocarbons, and organic fatty acids.

Some ordinary building materials such as concrete, drywall, or insulation have been engineered over the past 50 years to contain phase change materials’ microscopic pellets. Cellulose insulation is commonly used to insulate attics and walls.

Researchers at the Oak Ridge National Laboratories in the United States have impregnated small paraffin pellets in this common insulation type to increase its performance. Because these pellets are microscopic, the phase change insulation looks exactly like the ordinary insulation to our naked eye. However, under a Scanning Electron Microscopic, the clusters of paraffinic pellets are easy to spot.


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Sources:

Bryan, G.H. Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications.
Maxwell, J.C. Theory of Heat, third edition, Longmans, Green, and Co., London.
Harper, Douglas. “latent.” Online Etymology Dictionary.
Lewis, Charlton An Elementary Latin Dictionary. Entry for latent.
James Burke. “Credit Where It’s Due.” The Day the Universe Changed.

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