Heating Curves and the Relationship between Kinetic Energy and Temperature

[sgstudent]

When i heat up an object, the kinetic energy increases. But since kinetic energy can be converted into positive or negative potential energy when it vibrates, during the heating process how can we say that the KE increases and thus temperature increases since at different points of time, the KE of a particle might be 0 and PE be at maximum.

Also, during a state change, shouldn't the same process where by KE+PE=total energy of particle? But during a state change it seems that KE remains constant.

In my physics syllabus we weren't taught about that vibration thing but I learned about it on this forum. So I'm not sure how a heating curve actually works.

Thanks so much for the help

 

[DrClaude]

When i heat up an object, the kinetic energy increases.

For a gas, you can get basically a direct relationship between temperature and the kinetic energy of the molecules, but this is only strictly valid for a monatomic ideal gas. More generally, increasing the temperature corresponds to an increase in energy, but not necessarily kinetic.

In a simple model of a solid, you have to take into account that when heat enters the solid, it increases both the kinetic and potential energy of the vibrating atoms.

 

[sgstudent]

For a gas, you can get basically a direct relationship between temperature and the kinetic energy of the molecules, but this is only strictly valid for a monatomic ideal gas. More generally, increasing the temperature corresponds to an increase in energy, but not necessarily kinetic.

In a simple model of a solid, you have to take into account that when heat enters the solid, it increases both the kinetic and potential energy of the vibrating atoms.

Hi thanks so much for the help :)

Ohh so it's like since the solid has more energy the both the average potential and kinetic energy would have to increase? Is that why generally solids and liquids expand as the potential energy increases too? But since potential energy can be negative or positive why would the expansion be more predominant here?

Lastly, what about state change? Since again I'm putting in energy, shouldn't the kinetic and potential energy increase as an average too?

 

[DrClaude]

Ohh so it's like since the solid has more energy the both the average potential and kinetic energy would have to increase? Is that why generally solids and liquids expand as the potential energy increases too?

Think of it in terms of total energy. As you increase the energy, the system gets farther away from the minimum energy state, and in most cases this corresponds to an increase in the size of the system. In a simple picture again, think of the atoms inside the solid as being connected by springs. As the energy increases, the amplitude of the oscillation of the atoms around their equilibrium position increases, such that an atom pushes more against its neighbors, and the substance expands.

But since potential energy can be negative or positive why would the expansion be more predominant here?

I didn't address this previously, but energy cannot be negative! That said, in most physical problems, only relative energy values are important, such that you can set the zero of energy arbitrarily. For instance, for molecules it is often the case that the zero of energy is set for the case where all bonds are broken and the atoms are free. A negative potential energy in this case corresponds to an energy below that of dissociated atoms, and thus to a stable molecule. But the energy itself is a positive quantity. And in many cases, like the harmonic oscillator (the basis for the simple model of a solid I am using here), the zero of energy is chosen to be at the minimum (equilibrium position), so even the relative energy is always positive.

Lastly, what about state change? Since again I'm putting in energy, shouldn't the kinetic and potential energy increase as an average too?

During a phase change, the energy goes into separating the atoms or molecules apart. You basically have to counter the attraction between the atoms/molecules to, for example, go from a solid to a liquid.

 

[sgstudent]

Hi thanks this helps a lot. But won't the increased expansion be equal to the increased contraction as the vibration is greater? So I'm thinking that there isn't a 'net' change so I shouldn't observe any expansion. But then again in real life most solids, liquids and gases expand when heated (for gases I'd guess that PV=nRT would be used to calculate the expansion).

Also for the state change, I don't understand what's the difference between regular heating whereby the average KE increases as more energy is put in the maximum KE increases, while during a state change, since heat is still supplied why doesn't the average KE increase? Since when I put in more energy it also can be converted from KE to PE as well like in the heating process?

Lastly, since the energy I put in is a positive value could you explain how during the contraction process it would still be positive?

Thanks so much for the help :) greatly appreciate it :)

 

[DrClaude]

But won't the increased expansion be equal to the increased contraction as the vibration is greater? So I'm thinking that there isn't a 'net' change so I shouldn't observe any expansion.

What contraction? If oscillations around the equilibirum point have a greater amplitude, each atom takes up more space, and the overall solid as to be bigger.

But then again in real life most solids, liquids and gases expand when heated (for gases I'd guess that PV=nRT would be used to calculate the expansion).

Yes, the ideal gas law is a good model for gases. If T increases at constant P, V must increase.

Also for the state change, I don't understand what's the difference between regular heating whereby the average KE increases as more energy is put in the maximum KE increases, while during a state change, since heat is still supplied why doesn't the average KE increase?

It's not that KE cannot increase, it's just that it's more complicated during a phase transformation, where interactions play a big role. I imagine that if you make the calculation, you will find that the gas has more KE than the liquid at the boiling point. What I really wanted to stress is that saying that more T means more KE is only really meaningful for a gas, and KE is not how temperature is defined.

Lastly, since the energy I put in is a positive value could you explain how during the contraction process it would still be positive?

I don't understand: what contraction?

 

[sgstudent]

What contraction? If oscillations around the equilibirum point have a greater amplitude, each atom takes up more space, and the overall solid as to be bigger.Yes, the ideal gas law is a good model for gases. If T increases at constant P, V must increase.It's not that KE cannot increase, it's just that it's more complicated during a phase transformation, where interactions play a big role. I imagine that if you make the calculation, you will find that the gas has more KE than the liquid at the boiling point. What I really wanted to stress is that saying that more T means more KE is only really meaningful for a gas, and KE is not how temperature is defined.



I don't understand: what contraction?

Hi thanks for the great reply :)

I thought if I had more energy both the expansion and contraction would increase? The idea I had was that the solid would oscillste left and right so the particles on either sides will both expand and contract when they are heated. But it seems that's the wrong mental picture. Could you explain further how it would expand?

Oh so during a phase change it gets more complicated. But still shouldn't temperature be the average kinetic energy?

Thanks so much for the help provided :)

 

[DrClaude]

I thought if I had more energy both the expansion and contraction would increase? The idea I had was that the solid would oscillste left and right so the particles on either sides will both expand and contract when they are heated.

For contraction to happen, you would need all the atoms to move in a concerted fashion. If the movements are random, then all you need to take into account is the average atom-atom distance, which increases with vibrational energy.

Oh so during a phase change it gets more complicated. But still shouldn't temperature be the average kinetic energy?

No, you have to consider total energy, not just kinetic energy. Think about it: you have coexistence of liquid water and steam at 100°C, so both have the same temperature. Do you think that a molecule of water has the same kinetic energy in the liquid and the gas phase?

 

[sgstudent]

For contraction to happen, you would need all the atoms to move in a concerted fashion. If the movements are random, then all you need to take into account is the average atom-atom distance, which increases with vibrational energy.
No, you have to consider total energy, not just kinetic energy. Think about it: you have coexistence of liquid water and steam at 100°C, so both have the same temperature. Do you think that a molecule of water has the same kinetic energy in the liquid and the gas phase?

That's where I'm unsure of how heat affects KE or PE. I learned about specific best capacity and latent heat of vaporization. So for Q=mcT I would guess that that's the energy absorbed but I'm not sure how it increases the temperature. It absorbs that energy and some of of goes to the new PE and some KE? While for Q=ml I'm not sure where that energy goes to. I know it has to have more energy but I'm not sure if it just goes into the potential energy aspect of it though.

Thanks again :) this has been confusing me for a while now