I am rather perplexed around this. I understand from Charles" law that under constant pressure, the volume of a gas is directly proportional to its absolute temperature i.e.

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$$fracV_1T_1 = fracV_2T_2$$

Hence appropriately, throughout compression, temperature of the gas would decrease. But in Lectures of steustatiushistory.org ,vol 1 by Feynguy, it is written:

Suppose that the piston moves inward, so that the atoms are slowly compressed right into a smaller sized room. What happens once an atom hits the moving piston? Evidently it picks up speed from the collision. <...> So the atoms are "hotter" once they come away from the piston than they were prior to they struck it. Therefore all the atoms which are in the vessel will certainly have actually picked up speed. This suggests that as soon as we compush a gas progressively, the temperature of the gas increases.

(Constant pressure?) So, this is contrary to Charles" law. Why does this happen? Who is right? Or are they both correct? I am perplexed. Assistance.

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thermodynamics push temperature ideal-gas volume
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edited Mar 19 "19 at 5:39

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asked Sep 20 "14 at 13:24
$egingroup$ So tright here are various conditions? .... Is not Charles' legislation speaking of gas'pressure? What is Feynmale talking of ? $endgroup$
Sep 20 "14 at 13:40
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There"s actually not one simple answer to your question, which is why you are a bit perplexed. To specify your difficulty completely, you need to specify specifically how and also whether the gas swaps warm through its surroundings and also just how or even whether it is compressed. You have to constantly describe the full gas regulation $P,V=n,R,T$ as soon as reasoning. Usual situations that are considered are:

Charles"s Law: The pressure on the volume gas is constant. No work-related is done by the gas on its surroundings, nor does the gas perform any kind of job-related on its surroundings or piston or whatever before throughout any adjust. The gas"s temperature is that of its surroundings. If the ambient temperature rises / drops, heat is moved into / out from the gas and its volume appropriately boosts / shrinks so that the gas"s pressure deserve to stay constant: $V = n,R,T/P$; through $P$ continuous, you deserve to retrieve Charles"s Law;

Isothermal: the gas is compressed / expanded by doing work-related on / permitting its container to execute work on its surroundings. You think of it inside a cylinder with a piston. As it does so, heat leaves / comes into the gregarding save the temperature continuous. As the gas is compressed, the job-related done on it reflects up as raised internal energy, which must be transferred to the surroundings to store the temperature continuous. At constant temperature, the gas legislation becomes $Ppropto V^-1$;

Adiabatic: No warm is transferred in between the gas and also its surroundings as it is compressed / does job-related. AGain, you think of the gas in a cylinder with a plunger. This is prototypical case Feynguy talks around. As you press on the piston and change the volume $Vmapsto V- m dV$, you do work-related $-P, m dV$. This power stays via the gas, so it should show up as enhanced inner power, so the temperature need to climb. Get a bicycle tyre pump, host your finger over the outlet and also squeeze it difficult and also fast via your various other hand: you"ll find you have the right to heat the air up inside it rather substantially (put you lips gently on the cylinder wall to feeling the increasing temperature). This case is explained by $P, m dV = -n, ildeR, m d T$. The internal energy is proportional to the temperature and also the number of gas molecules, and it is negative if the volume rises (in which instance the gas does job-related on its surroundings). But the consistent $ ildeR$ is not the very same as $R$: it relies on the interior levels of flexibility. For circumstances, diatomic molecules can keep vibrational and also kinetic power as their bond size oscillates (you can think of them as being organized together by elastic, energy storing springs). So, as soon as we usage the gas law to remove $P = n,R,T/V$ from the equation $P, m dV = -n, ildeR, m d T$ we gain the differential equation:

$$frac m d VV = - frac ildeRRfrac m d TT$$

which integrates to yield $(gamma-1),log V = -log T + extconst$ or $T,V^gamma-1 = extconst$, wright here $gamma=fracR ildeR+1$ is dubbed the adiabatic index and is the ratio of the gas"s particular heat at continuous pressure to the specific warm at continuous volume.