[INCOMPLETE ]Thermodynamics Stupidisation - Thermodynamic Processes

Okay now i'm done with characterising the ideal gas.

oops...forgot abt PV = nRT
Ideal gas equation is a relation between the macro parameters of a gas. The relation was deduced by experiment, thanks to Charles, Boyle, Guy-Lussac...who else? hmm anyway, in the previous post i've shown the equation relating the pressure to macro level parameters...which essentially is the speed of the gas particles! Equating the macro and micro equations, we have the following:
1/2Nm = 3/2NkT

Rearranging for T, we also see that temperature is due to the speed of the gas particles.

So, the implications of a gas consisting of particles moving at a certain average speed, is that, it has a certain temperature, and exerts a certain pressure, and occupies a certain volume...nice cause and effect!...

wait! i think we gotta interpret this volume-pressure thing really carefully...its quite lame talking about a gas occupying a certain fixed volume, if its not bounded by a container...after all, the gas is gonna dissipate if there was no container to hold it! How then can we talk abt volume and pressure? I think we should amend the statement above to this instead:

Given a gas consisting of particles with a total amt of internal energy U (solely kinetic energy, cos its an ideal gas we're talking abt), there is a relation between the volume in which the gas is being enclosed inside (by means of a container), the pressure it exerts, and its temperature. This relation is, well,
PV = nRT

rearranging, gives T = PV/nR
shit...how can increasing V increase temperature? NO WAY! NOt unless i give the gas energy!!
damn...so how to interpret PV = nRT? argh!!!

okay lets look at other cases (variable that's not discussed assumed to be kept constant):
P = nRT/V - increase temperature, increase pressure...well that works fine. but inc. temp must be due to some energy input right?
increase volume, decreases pressure...that's true...
V = nRT/P - increase temp, increases volume...

BUt increase volume doesn't increase temperature! unless there's energy input! argh whatever this is all getting very confusing...i suppose this is where thermodynamic processes come in...

okay...i think i get it...PV=nRT still remains true...if i could just increase volume while keeping pressure constant, temperature has to increase! Just think abt the microscopic level of things...if the gas needs to exert the same pressure, ie. the same force on the walls, the particles have gotta move faster to keep up the same rate of collision with the walls!

hence PV = nRT is an empirically proven relation between the variables of a gas. And it is logically consistent! How certain things can happen, such as increasing the volume while maintaining the pressure constant, and hence increasing the temperature, is not the business of the ideal gas equation. It just tells us that if we want to do this, the consequence has gotta be temp. increase. The rest of thermodynamics tells us how we can accomplish this.

In fact, this is in essence, the First Law of Thermodynamics! So, we want to increase volume, at constant pressure...that's called an isobaric process. For this to happen, the particles must move faster. That means more kinetic energy, hence this means the internal energy of the gas must increase! By the conservation of energy, this energy must be supplied from some source outside of the system. This implies that all our heat energy goes to increasing temperature...but we must be careful! But we first note that the first law of thermodynamics is an expression of the conservation of energy in a close system involving a gas.

We could supply heat energy so that both temperature and volume increase at constant pressure. Now that's isobaric. So what happens is that some heat energy is used by the gas to do work in expanding...the rest goes to increasing the KE of gas particles, and hence its temperature.

Another possible way is to first increase the volume, perhaps by pulling out the plunger of a syringe, and then then heating it to cause an increase in temperature. That would be TWO processes. Increasing the volume would do negative work on the gas...i.e. the gas loses internal energy. Then heating it at constant temperature would give