How does the distance between molecules affect temperature?

[TT0]

Homework Statement

According to the kinetic molecular theory:

1. as the distance between the molecules increases, the temperature of a material decreases
2. the rise in temperature of a material occurs because the molecules lose kinetic energy
3. when the molecules within a gas collide they lose energy, reducing the temperature of the gas
4. the molecules within all liquids and gases are always in motion, but not in solids.
   

Homework Equations

The Attempt at a Solution

I said 4 because liquids and gases have translational energy while solids dont. However, the answer is 1. Can someone explain how does the distance between molecules affect temperature?

Cheers!

 

[ehild]

Homework Statement

According to the kinetic molecular theory:

1. as the distance between the molecules increases, the temperature of a material decreases
2. the rise in temperature of a material occurs because the molecules lose kinetic energy
3. when the molecules within a gas collide they lose energy, reducing the temperature of the gas
4. the molecules within all liquids and gases are always in motion, but not in solids.

Homework Equations

The Attempt at a Solution

I said 4 because liquids and gases have translational energy while solids dont. However, the answer is 1. Can someone explain how does the distance between molecules affect temperature?

Cheers!

The molecules of a solid are always in motion, too. They vibrate about their equilibrium position.
The statement 1 is valid only if the expansion of the object is adiabatic. The object can expand when heated and then the average distance between the molecules also increases, while the temperature increases.

 

[TT0]

I see thanks!

 

[lychette]

The Kinetic theory of gases assumes that collisions between molecules are perfectly elastic i.e No Ke is lost in collisions so this rules out 2 and 3 and sensible options.
The main aim of the Kinetic theory is to develop an expression/explanation for the pressure exerted by a gas. At some stage you shoul;d have an expression
P = (2N/3V)mc²/2 where m is the mass of a molecule, c is the speed of a molecule, N is the number of molecules and V is the volume occupied by the N molecules. The quantity mc²/2 is a measure of temperature (T)
This means that...FOR THE SAME PRESSURE..a smaller number of molecules in the same volume (greater separation) corresponds to a lower temperature.
I think that 1 is the correct answer.
I agree with ehild, molecules in a solid are in motion...they are vibrating

 

[ehild]

The main aim of the Kinetic theory is to develop an expression/explanation for the pressure exerted by a gas. At some stage you shoul;d have an expression
P = (2N/3V)mc²/2 where m is the mass of a molecule, c is the speed of a molecule, N is the number of molecules and V is the volume occupied by the N molecules. The quantity mc²/2 is a measure of temperature (T)
This means that...FOR THE SAME PRESSURE..a smaller number of molecules in the same volume (greater separation) corresponds to a lower temperature.

In case of less number of molecules in the same volume the pressure stays the same if the average KE of the molecules is higher, that is, the temperature is higher.

 

[lychette]

In case of less number of molecules in the same volume the pressure stays the same if the average KE of the molecules is higher, that is, the temperature is higher.

quite correct...rephrase my statement..' the same number of molecules in a bigger volume gives a lower pressure and lower temp'
I think this is the best answer. ie option 1

 

[mpresic]

This is a very poorly worded question. Increasing the distance between the molecules does not in and of itself, decrease the temperature of the material. It is the other way around. As the temperature of the material increases, the distance between the molecules usually increases. Molecules in a solid move as well. Even if they do not translate, or rotate, they vibrate. 2 and 3 are clearly incorrect answers.

An interesting thought concerning the kinetic molecular theory. Temperature is the average kinetic energy of the "molecules" or constituents of matter. Suppose you have a million molecules in a (small) drop of water with average kinetic energy T. Now suppose you have a million stars in a (small) galaxy with the same kinetic energy T. Would they not be the same temperature?

 

[ehild]

quite correct...rephrase my statement..' the same number of molecules in a bigger volume gives a lower pressure and lower temp'
I think this is the best answer. ie option 1

If it is an ideal gas, PV=NkT, N is the number of molecules and k is the Boltzmann constant. Keeping the number of molecules constant, the increase of their distance means increase of the volume. T=PV/(Nk). If V increases T can increase, decrease, or stay constant, depending on the relation between P and V. It can be an isotherm process, T=constant and P decreases. It can be an isobaric process, P=constant, then T increases as V increases. And in an adiabatic process, when the change of internal energy is due to the work done by the gas on the surrounding, ΔU =C_VΔT = -PΔV, the temperature decreases when the volume increases. So statement 1 can be true or not. The other statements are all false.

 

[lychette]

from the point of view of molecules in an expanding container those molecules sriking the walls of the container will rebound with reduced speed. The average speed of molecules in the container will tend to decrease.
Because of the expansion the average distance between molecules will increase.
For the gas this means that the average temperature tends to decrease and the pressure tends to decrease (there are fewer collisions per second with the walls of the container).
The external conditions determine whether the temp of the gas will be observed to decrease. Slow expansion in good thermal contact with the surroundings will enable heat energy to pass into the gas and the temp will remain constant, this is isothermal expansion.
Fast expansion in a thermally insulated container will cause the temperature and pressure to decrease, this is adiabatic expansion.
It is clear that the correct response is number 1. 2,3 and 4 are readily dismissed.