Temperature and Internal Kinetic Energy

Sorry, that doesn't sound too clear^^.

(P1)(V1)/[(T1)(N1)] = (P2)(V2)/[(T2)(N2)]

solve for T2:

T2 = P2/P1 x V2/V1 x N1/N2 X T1

We want T2>T1, so
P2/P1 x V2/V1 x N1/N2 > 1

We already know that the kinetic energy decreased, so the pressure decreased.

First of all, heat is just kinetic energy per unit volume. A hot object is one that has a lot of molecular motion. Kinetic energy is a more general term because it can also be used to describe macroscopic motion (eg, not just molecular motion).



The professor is correct. Clearly, temperature depends on other variables. However, when asking a question like this, it is implied that all other things remain equal. Furthermore, when talking about reducing the kinetic energy of a substance, it is implied that you are doing so by reducing the speed of the constituent particles. Since this is the definition of heat, by definition, temperature is reduced.



T = (pV)/(nR)

The teacher didn't say to change the volume or the amount of substance. Therefore, a reduction of kinetic energy simply reduces the pressure. Clearly, this action results in a smaller T (temperature).

Pressure and volume are not independent variables in this equation. Intuitively, you would think that if you decreased the volume, the temperature would increase -- but the equation seems to indicate otherwise, doesn't it? That is because reducing the volume by 50% would increase the pressure by more than 50%, which is a net increase. Similarly, increasing the number of molecules would increase the pressure unless the molecules all slowed down.

No, he didn't say change volume or pressure or w/e. But in a previous question "If you add heat does the temperature rise?" He said no, as, if negative work is done on the gas, by increasing the volume, say, then the temperature does't necessarily increase; why should it be any different this time, in terms of changing other conditions?

I understand preessure and volume are inversely related at constant T, so a drop in pressure and a drop in volume, what would that do? Inreasing the number of molecules increases pressure, increases temperature, isn't that what we want?
Temperature is related to the internal kinetic energy insofar as the gas molecules collide with their container, either changing the number of collisions (volume or no. of molecules) or the speed of the molecules (internal kinetic energy) changes the temperature?

Heat is the transfer of thermal energy. Temperature is a measure of the thermal energy. So if heat energy is flowing in, then temperature is increasing by definition. If you have quoted your teach accurately, then he is wrong. However I find it more likely that some of what he was saying to you was lost in translation.



If you decrease pressure or volume independently, temperature drops. If you decrease them together, temperature still drops.



I'm not sure...what do we want?

lol, nvm, I'll sort this out, thank you anyway, for always answering my questions

For closure: You are correct stuh. For ideal gases the temperature depends only on internal energy. If the gas is mono-atomic the only internal energy is translational kinetic. For non-mon-atomic ideal gases there is also rotational and vibrational energy. Gravitational potential energy is negligible.
For real gases internal energy is larger at high pressure/low volume due to inter-atomic forces and the fact that real gases occupy a significant proportion of the total volume.
It's interesting that in adiabatic changes of volume the temperature remains constant (no-Q), but the entropy still changes as the volume in which the gas is contained is changing.