Have you ever wondered how much energy is needed to boil water? If you like cooking, you should know that it would take a long time for a pot of water to boil off. You might have heard that water boils at, but if you measure the temperature of the water as it starts bubbling, you can see that it is already at boiling temperature. Why hasn't it all become vapour already? Moreover, if you leave the thermometer inside the water, you will see that is it not getting any hotter, even if the stove is still on. Where is the energy going?
There is a lot of physics in our daily activities and sometimes we consider what happens around us as normal without thinking about it. If these questions have you scratching your head, there is no need to worry. It might all sound a bit confusing now, but the key to answering all of the previous questions lies in how heat affects the internal energy of a substance. We will explain the relationship between the heat provided to a system and its internal energy, and it will lead us to the concept of specific latent heat.
Heat and Internal Energy
Internal energy is the sum of the individual kinetic and potential energies of the particles (atoms or molecules) that make up a system.
The temperature of a system is a measure of the kinetic energy of its particles. It only depends on how fast they are moving or vibrating. On the other hand, the system's potential energy depends on how the particles are bonded together, and thus it's related to the state of the system. When we heat a substance, we provide it with energy, but this can happen in two ways:
1. Increasing the temperature of the system. The particles comprising the system gain kinetic energy, moving faster and resulting in an increment of the system's temperature. This is what happens to the atoms of iron in a pan when it is heated on a stove, at the atomic level.
2. Changing the state of the system. The energy provided can also be used to break or change the bonds between the particles of the system. In general, this allows the particles to move farther apart, increasing the potential energy stored in the system and resulting in a new state. This is what usually happens when solids melt.
As the change of state occurs the potential energy of the particles increases.
Similarly, when the substance boils, the intermolecular bonds break again it becomes a gas. When a substance is in a gas state, its molecules try to stay away as much as possible from each other.
After a liquid becomes a gas, its particles tend to stay as far as possible from each other.
Keep in mind that in both cases, the internal energy increases as it is the sum of the kinetic and the potential energy. Therefore, as long as one of them increases, their sum increases as well. Now that we understand how, it is essential to understand when each of these energies increases as we heat our system:
As long as the system remains in the same state, its potential energy will not change. Only the kinetic energy increases, and thus its temperature.
When a change of state is occurring, all the energy is used to break or change the bonds between the particles of the system and increase their separation. Since the kinetic energy of the particles does not change, the temperature of the system remains constant during a change of state.
The graph below shows how the temperature of a kilogram of water changes as energy is provided.
When water is changing state, the temperature remains the same even if more energy is supplied. The flat lines represent this. On the other hand, when no state transition is occurring, the energy is used to increase the temperature of the water, as represented by the blue line segments with a positive gradient. Enrique Vizcarra Carrazco - StudySmarters Originals
Take a look at the middle part of the graph, where water is liquid. As energy is supplied, its temperature continues to increase until it reaches a critical value for the next state transition - vaporization. Even when the water has reached its boiling temperature,, it still needs energy for the transition from liquid to gas to occur. This is why when we heat water to this temperature, it does all not become vapour at once. Moreover, once the water has reachedall energy is used to turn it into vapour, keeping the temperature constant.
Great! With all this information, we have a good understanding of how heat affects a system. We have already solved most of the questions at the begging this article, except for one: exactly how much energy is needed to make water boil? This can be answered by introducing the concept of specific latent heat.
Definition And The Formula for Specific Latent Heat
Specific latent heat is the amount of energy required to change the state ofof a substance without changing its temperature.
The specific latent heat changes from substance to substance. It can be determined experimentally using the following formula
wereis the specific latent heat,is the energy andis the mass.
Specific Latent Heat Units
As indicated by the previous formula, the specific latent heat is obtained as the ratio of the energy needed for the state transition to the mass. Therefore, it has derived units obtained by dividing the units of energy by the units of mass. In the SI energy is measured in joulesand mass in kilograms. Hence the units for specific latent heat are
.
Specific Latent Heat Equation
If the specific latent heat and the mass of a substance are known, we can calculate the amount of heat needed for the change of state by using the specific latent heat equation with the energy isolated.
In the above equation,is the energy in joules, the specific latent heatis in joules per kilogram, andthe mass is in kilograms. Considering the states: solid, liquid, and gas, we can have two different transitions. Therefore, we have two different values for the specific latent heat to consider.
Specific Latent Heat of Fusion
Specific latent heat of fusion is the energy required to change a substance from solid to liquid at a constant temperature.
It is important to mention that the same amount of energy needs to be released by the system to go from liquid to solid. For example, the specific latent heat of fusion of water is. This means that to melt one kilogram of ice we need to provide, but if we want to freeze a kilogram of water, we need to subtractfrom it instead.
The specific latent heat of fusion of water tells us how much energy we need to provide to melt a kilogram of ice. Conversely, we can freeze one kilogram of water by subtracting the same amount of energy from water. StudySmarter Originals
Recall that for the transition to occur, the substance has to be at its fusion temperature. The following table shows the specific latent heat of fusion for some substances.
| Substance | Specific latent heat of fusion |
| aluminium | 396,000 |
| gold | 63,000 |
| iron | 247,000 |
| silver | 105,000 |
| water | 334,000 |
| zinc | 112,000 |
You might be surprised to notice that water requires more energy to melt than most of the other substances shown. However, note that the specific latent heat of fusion has nothing to do with the fusion temperature! For example, to melt a kilogram of water, it is required around five times the energy to melt one kilogram of gold. However, the temperature at which water melts iswhile gold melts at.
Calculate the energy needed to meltof ice at.
Since the mass is given and the specific latent heat of fusion for water is known, we can calculate the energy using the equation introduced before.
Now let's substitute the known values and simplify.
Therefore, we need to provideof energy to melt theof ice.
States transitions require a lot of energy. But, in particular, water is well known for having a high specific latent heat value. This means that a block of ice requires to 'absorb' a lot of heat from the environment to melt down. Before refrigerators were available, people took advantage of this property of water and used big blocks of ice to preserve food, cool drinks, and create frozen desserts. There were jobs that consisted in cutting ice from frozen lakes and delivering them to homes. This was called ice harvesting.
The ice industry depended entirely on the weather, and big blocks of ice were obtained from frozen lakes, rivers, and ponds.
After the delivery, the block of ice was put inside special furniture called 'iceboxes.'
Iceboxes were used t isolate the ice and goods from the environment, preserving food and cooling drinks.
Since creating ice depended entirely on the weather, ancient Persians developed a conical structure that could isolate the ice collected during the winter. Not only that, since hot air is less dense than colder air, the structure also helped to let the cooler air sink down into a pit while the warmer air went up and got channelled by its shape and was released into the outside. With these structures, they could keep the ice collected during the winter all year long!
The conical shape helped to channel the hotter air outside leaving the cooler air trapped inside. This mechanism together with the insulation provided makes it possible to keep ice for months.
Specific Latent Heat of Vaporization
The specific latent heat of vaporization is the energy required to change a substance from liquid to gas at a constant temperature.
For a state change from gas to liquid, the energy should be subtracted from the substance instead of being added. The following table shows a few examples of substances and their specific latent heat of vaporization.
Substance | Specific Latent Heat of Vaporization |
aluminium | 10,900,000 |
gold | 1,645,000 |
iron | 6,090,000 |
silver | 2,390,000 |
water | 2,256,000 |
zinc | 1,890,000 |
WASP-121 b is a planet located 880 light-years away from Earth. It is so hot that iron evaporates and forms clouds. However, during the planet's night, the temperature drops enough for liquid metal to rain. Consider acloud of iron in this planet. How much energy does the cloud need to give so that it can rain as liquid iron?
From the previous table, we can see that the specific latent heat of vaporization of iron is. Let's substitute this value and the known mass in the equation for the energy and simplify.
Because the resulting amount is so big it is convenient to express it using scientific notation.
Therefore, the cloud of iron needs to release into the atmosphere as heat in order to be able to rain in liquid form.
Specific Latent Heat - Key Takeaways
- The internal energy of a system is the sum of the individual kinetic and potential energies of its particles (atoms or molecules).
- The temperature of a substance is a measure of the kinetic energy of its particles or molecules.
- During a change of state, the temperature of the system does not change. Any energy input goes to breaking or changing the bonds of the system's particles and or moving farther apart, storing potential energy.
- The specific latent heat of fusion is the energy that needs to be provided to one kilogram of a substance for it to change from solid to liquid, at a constant temperature. For the substance to change from liquid to solid, it needs to release the same amount of energy to the environment.
- The specific latent heat of vaporization is the energy that needs to be provided to one kilogram of a substance for it to change from liquid to gas, at a constant temperature. For the substance to change from gas to liquid, it needs to release the same amount of energy to the environment.
- The equation for the specific latent heat of fusion and the specific latent heat of vaporization is identical:. We use the specific latent heat of fusion or vaporization depending on the change of state that is taking place.
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