What is the change in average kinetic energy of molecules of a solid during melting at its melting point?

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The term 'change of phase' means the same thing as the term 'change of state'.

There are four states, or phases, of matter:

We will not be discussing the plasma state here.

When a substance changes from one state, or phase, of matter to another we say that it has undergone a change of state, or we say that it has undergone a change of phase. For example, ice melts and becomes water; water evaporates and becomes water vapor.

These changes of phase always occur with a change of heat. Heat, which is energy, either comes into the material during a change of phase or heat comes out of the material during this change. However, although the heat content of the material changes, the temperature does not.

Here are the five changes of phase. They are diagrammed in the opening animation and listed below.


Solid to liquid	Melting	Heat goes into the solid as it melts.	None
Liquid to solid	Freezing	Heat leaves the liquid as it freezes.	None
Liquid to gas	Vaporization, which includes boiling and evaporation	Heat goes into the liquid as it vaporizes.	None
Gas to liquid	Condensation	Heat leaves the gas as it condenses.	None
Solid to gas	Sublimation	Heat goes into the solid as it sublimates.	None

So, how could there be a change in heat during a state change without a change in temperature? During a change in state the heat energy is used to change the bonding between the molecules. In the case of melting, added energy is used to break the bonds between the molecules. In the case of freezing, energy is subtracted as the molecules bond to one another. These energy exchanges are not changes in kinetic energy. They are changes in bonding energy between the molecules.

If heat is coming into a substance during a phase change, then this energy is used to break the bonds between the molecules of the substance. The example we will use here is ice melting into water. Immediately after the molecular bonds in the ice are broken the molecules are moving (vibrating) at the same average speed as before, so their average kinetic energy remains the same, and, thus, their Kelvin temperature remains the same.

Below is a picture of solid ice melting into liquid water. The molecule of ice and the molecule of water (the black balls) are moving with the same rate of vibration in this diagram. This is meant to show that they have the same average speed and thus the same average kinetic energy (since they have the same mass) and thus the same Kelvin temperature. The motions are, though, greatly exaggerated. Actually, the motions of the molecules should be considered tiny vibrations.

At the moment of melting the average kinetic energy of the molecules does not change.The heat is used to break the bonds between the ice molecules as they turn into a liquid phase. Since the average kinetic energy of the molecules does not change at the moment of melting, the temperature of the molecules does not change.

Since both the ice and the water molecules have the same average kinetic energy at the time of melting, the temperatures of both are the same.

Click this button to see the computer code for this animation.

Here's the code that runs the above animation.

You can change the code, if you like, and then click the following 'Reevaluate code' button. The program will then work as per your changes. Of course, your changes, especially random changes, can introduce errors, miscalculations, and browser crashes. If you need to get things back to their original condition, just reload this page using your browser's reload button.

The intention here is to conveniently show the inner workings of this program so that you understand how the diagram is drawn. Can you figure out how to change the code to make the molecules vibrate at a higher frequency?

Click the 'Code' button again to close this section.

// change of state var loopWait = 50; // ms. var iceXO; // original x-coordinate var iceYO; // original y-coordinate var iceX; // current x-coordinate var iceY; // current y-coordinate var waterXO; var waterYO; var waterX; var waterY; // molecule vibration var amplitude; // amplitude, both molecules var fx; // x-frequency, both molecules var fy; // y-frequency, both molecules var phase; // phase offset for water molecule var t; // current time var dt; // delta time var twoPi = 2 * Math.PI; setup = function() { // original position for ice molecule iceXO = 140; iceYO = 120; // original position for water molecule waterXO = 170; waterYO = 195; fx = 2; // x-frequency for both molecules fy = 3; // y-frequency for both molecules amplitude = 10; // amplitude of vibration for both molecules phase = 1; // phase of vibration for water molecule t = 0; // current time dt = .1; // delta time }; loop = function() { // find new positions for molecules update(); // draw molecules at new positions render(); // wait a bit, do it again loopTimeout = setTimeout(loop, loopWait); }; update = function() { // this math moves the molecules in a Lissajous figure // calculate molecule positions at the current time iceX = Math.floor(iceXO + amplitude * Math.sin(fx * t)); iceY = Math.floor(iceYO + amplitude * Math.sin(fy * t)); // phase shift water molecule vibration // the motions are identical, except one lags behind the other waterX = Math.floor(waterXO + amplitude * Math.sin(fx * t + phase)); waterY = Math.floor(waterYO + amplitude * Math.sin(fy * t + phase)); t += dt; // tic the clock to the next time for the next update // keep the time between 0 and two times pi // since two times pi is the natural period of the sine function if(t > twoPi) t -= twoPi; }; render = function() { // position DOM images iceImg.css('left', iceX.toString() + 'px'); iceImg.css('top', iceY.toString() + 'px'); waterImg.css('left', waterX.toString() + 'px'); waterImg.css('top', waterY.toString() + 'px'); };

In the ice the molecules are strongly bonded to one another, thus forming a rigid solid. When heat is added to the ice these bonds are broken and the ice melts. The molecules afterward bond to one another with less strength and a different geometry, and water is formed.

Now, before the melting, the molecules were actually moving when in the solid state. They were vibrating back and forth. They had an average kinetic energy. So they had a Kelvin temperature proportional to this average kinetic energy.

After the melting the water molecules are still vibrating. And they have the same average kinetic energy as they had before the melting. So, the water is at the same temperature at the moment after the melting that the ice was at the moment before the melting.

Heat came into the situation, but it was not used to change the kinetic energy of the molecules. It was used to change the bonding between the molecules. Breaking the bonds between the molecules of the ice requires energy, and this energy is the added heat.

In a similar way heat enters a liquid to change the molecular bonding when the liquid boils or evaporates into a gas, and heat enters a solid to change the molecular bonding when it sublimates into a gas.

In an inverse way heat leaves a gas to change the molecular bonding when the gas condenses into a liquid, and heat leaves a liquid to change the molecular bonding when it freezes into a solid.

In none of these changes of state is the heat (energy) that is input or output used to change the speed of the molecules. The average speed of the molecules is the same before and after a phase change, and so is the average kinetic energy.

Heat (energy) is transferred into the ice.

The heat is used to break the bonds between molecules, not to increase the average kinetic energy of the molecules.

Since the bonds among the ice molecules have been broken, water is formed. The water molecules, at this moment, have the same average kinetic energy as they did when they were ice.

Since the ice and water molecules both have the same average kinetic energy, they are at the same Kelvin temperature.

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