Thermochemistry

[hypnosis3000]

I'm having trouble understanding how both of the following statements make sense without violating each other:

Charles Law- At constant pressure, the volume of a given mass of gas increases or decreases by the same factor as its temperature (i.e. the volume increases as the temperature increases).

Expanding gases cool and compressed gases warm.

I was looking over work=-PdeltaV and don't understand how the second statement does not contradict the first one. The P, Pressure, is constant and doesn't change, but the Volume changes, so shouldn't temperature change proportionally.

Could you please explain my misconceptions using the ideal gas law and/or anything else where both statements are kept valid.

Thanks

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[fizzgig]

the first statement is part of pvnrt, so that part makes sense as PV=nRT. if V increases and P stays the same, with the same number of moles, you must have added some energy to those molecules (T inc). 10 balls bouncing around a small box will hit the sides enough to give pressure P even if they have low avg energy (T). in a giant box, still with 10 balls, they're going to have to be flying around with a LOT of energy to still contact the walls enough to give that same pressure P. same in reverse, if T increases the balls' average energy and you want P to remain constant, you've got to make the box bigger so that you get fewer high energy collisions vs more low energy collisions, giving the same P.

the second case you present is probably not a constant P situation (the word 'compressed').

so, we've got pvnrt. if volume divided by 2 then pressure would double with pvnrt, right? crap, T would be the same, so something is missing here... the key i think is that pvnrt is good at describing the state of things, but if you compressed the gas you DID add energy during a PROCESS that pvnrt doesn't fully describe. the box walls moving inward added energy to every molecule that hit the walls during compression. if heat is not allowed to leave the system to make up for this, you've got higher energy collisions than expected, pressure is a little high, and temp is a little high. pvnrt still describes the end state accurately, the numbers are just slightly different if you keep that energy from work vs if you let it leave the system and keep T the same (an adiabatic process).

expanding gas is opposite, as the receding box walls rob molecules of a little energy during the expansion process. in the end, your avg kinetic energy is a little lower than expected, T and P are lower than if you did not take this process into account.

methinks.

 

[lorenzomicron]

To reconcile these two laws, in a nutshell, is that Charle's Law, or more so the ideal gas law, described the way temperature affects a gas system. Adding heat energy to the system will force the gases to expand in volume, because their molecules have more energy. Thus, expansion of the gas is the initial effect on the gas by adding heat.

However, as they expand, the gas gives off heat, i.e. the energy of the molecules gets lower and lower; the gas will then expand until it gives of enough heat to be in thermal equilibrium with the surroundings. That is, the the gas will give off heat while expanding until its temperature equals that of the environment, all other things being equal.

 

[hypnosis3000]

To reconcile these two laws, in a nutshell, is that Charle's Law, or more so the ideal gas law, described the way temperature affects a gas system. Adding heat energy to the system will force the gases to expand in volume, because their molecules have more energy. Thus, expansion of the gas is the initial effect on the gas by adding heat.

However, as they expand, the gas gives off heat, i.e. the energy of the molecules gets lower and lower; the gas will then expand until it gives of enough heat to be in thermal equilibrium with the surroundings. That is, the the gas will give off heat while expanding until its temperature equals that of the environment, all other things being equal.

Let me see if I understood the concept.

Your saying that the volume will expand with increasing temperature, but at some point in time the volume will expand at a decreasing rate (temperature and volume are still directionally related, but not in the same proportions); hence, expanding gases cool. The expansion will stop when the system is at thermal equilibrium with its surroundings.

If this is true, then how would I know which process is occurring when. The initial and final conditions make sense, but how can I tell when expanding gases start to cool? Is there a certain physical property for that i.e Boiling Pt?

 

[TieuBachHo]

1) Expanding gases cool and compressed gases warm.

Think of it in term of conservation of energy - the interchange between kinetic energy and heat energy. The closer the molecules are, the more heat they produce and thus warming the system. The farther apart they are, the less heat they produce and thus cooling the system (less chances of collision).

2)Charles Law- At constant pressure, the volume of a given mass of gas increases or decreases by the same factor as its temperature (i.e. the volume increases as the temperature increases).

When you cool a system, you reduce its internal energy and thus the volume decreases and vice versa. So at a constant pressure, the temperature and volume increase/decrease proportionally.

***Both statements have no contradiction unless you misinterpret it somewhere. The internal energy is constant in the 1st statement but not so in the 2nd statement.

Hope this can clear things up.

 

[IntelInside]

The 2nd part of your question is concept known as the joule-thompson effect.

- Adiabatic process: no heat exchange, q=0

o Non Free Adiabatic expansion; q = 0, ΔE = -W

a) the gas does work as it expands, which means that energy is leaving the gas; if there is no heat coming in to replace that energy, then the internal energy of the gas is falling.

b) Since microscopic KE is one component of the internal energy, if the internal energy is decreasing, the microscopic KE is decreasing (again, assuming the microscopic PE, which is the other part of internal energy, is not changing; in an ideal gas, which has no intermolecular interactions, then microscopic PE will not change). If the microscopic average KE decreases, then the temperature decreases.

o In Free adiabatic expansion; q = 0, W=0, ΔE = 0

a) So in a FREE adiabatic expansion, the gas does no work as it expands (since it's expanding against a vacuum), the internal energy of the gas remains the same!!

b) For an ideal gas, this means the temperature does not change.

c) Even though the internal energy is remaining the same, for a real gas, the temperature actually will fall,. That's because as the gas expands and the molecules get farther apart, since they have an attraction for each other, separating them must increase the microscopic PE of the gas. So if the total internal energy remains the same, but the microscopic PE is increasing, the microscopic KE must be decreasing. Therefore the temperature decreases

d) Pressure decreases for both ideal and real gases!!!

 

[docelh]

I think the big error you made is that you are trying to pigeonhole concepts that are only loosely related. You took some generally known observations, and then tried to incorrectly map them onto another theory.

Clearly, the cooling of expanding gases is most applicable in an open system. Ideal gas law is not an open system. The compression of gases apply to a closed system, and you introduce two variables (P, V) to see how they impact T, whereas in the first example, you looked at single variable correlation. Mathematically, T could increase or decrease depending on the relative increase of P vs. the relative decrease of V. So again, you took a related concept of work applied to a system and mapped it onto ideal gas law incorrectly.

 

[hypnosis3000]

I think the big error you made is that you are trying to pigeonhole concepts that are only loosely related. You took some generally known observations, and then tried to incorrectly map them onto another theory.

Clearly, the cooling of expanding gases is most applicable in an open system. Ideal gas law is not an open system. The compression of gases apply to a closed system, and you introduce two variables (P, V) to see how they impact T, whereas in the first example, you looked at single variable correlation. Mathematically, T could increase or decrease depending on the relative increase of P vs. the relative decrease of V. So again, you took a related concept of work applied to a system and mapped it onto ideal gas law incorrectly.

I think I'm closer in understanding the problem, but still not there yet. Even for the ideal gas law, I introduced two variables; at constant PRESSURE if the VOLUME increases then temperature rises.

I think the question at hand is how a closed system in the ideal gas law can increase energy. Or can it increase energy at all, since we don't violate the conservation of energy? It makes sense that in an open system, the surroundings impacting the system will cause it to have a change in energy. Also, why can't the compression of gases be in an open system?

 

[Phantastic]

Expanding gases cool because they are doing work on the environment. Compressed gases heat because they are having work done on them by the environment. Energy is allowed to flow here, between our system (gas) and surroundings (universe).

PV=nRT considers only the system. In a closed system (i.e. no work being done on environment by system, or by environment on the system), an increase in T or V causes a proportional increase in V or T, respectively.

I can see you understand why each case is justified, but really take a moment and understand how these two situations are discussing two different scenarios: PV=nRT is for describing the final or initial state, when some initial or final conditions are known. Expansion/contraction is a process.

 

[hypnosis3000]

Expanding gases cool because they are doing work on the environment. Compressed gases heat because they are having work done on them by the environment. Energy is allowed to flow here, between our system (gas) and surroundings (universe).

PV=nRT considers only the system. In a closed system (i.e. no work being done on environment by system, or by environment on the system), an increase in T or V causes a proportional increase in V or T, respectively.

I can see you understand why each case is justified, but really take a moment and understand how these two situations are discussing two different scenarios: PV=nRT is for describing the final or initial state, when some initial or final conditions are known. Expansion/contraction is a process.

I see the main difference being how the ideal gas law applies to closed systems and the expansion/contraction to an open system.

But how can ideal gas law apply without a change in the environment? Also, how does a closed system become larger in volume while not interacting with the surroundings ?
Don't say KE of the gas molecules increase, because they increase due to temperature, and rising temperature means that the system is interacting with the environment; therefore, then its an open system.

 

[fizzgig]

correct me if i'm wrong...

if you let a gas do work by expanding, it loses internal energy, temp down, BUT if you have that system in a bath of the original temp, then energy will flow in to raise the temp back up. you lost energy and you gained energy, temp is the same, and in this case all you're looking at is the initial and final state (as posted above). you don't know how things got that way, but you let the volume expand so you know that, you measured temp, and now you can calculate a new pressure. the 'state' vs 'process' idea is key.

 

[docelh]

Expanding gases cool because they are doing work on the environment. Compressed gases heat because they are having work done on them by the environment. Energy is allowed to flow here, between our system (gas) and surroundings (universe).

PV=nRT considers only the system. In a closed system (i.e. no work being done on environment by system, or by environment on the system), an increase in T or V causes a proportional increase in V or T, respectively.

I can see you understand why each case is justified, but really take a moment and understand how these two situations are discussing two different scenarios: PV=nRT is for describing the final or initial state, when some initial or final conditions are known. Expansion/contraction is a process.

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OP, this forum is for answering specific questions related to MCAT, not baby hand-holding or vicarious tutoring. Would suggest you hit the books more and put in the hard time thinking, like the rest of us.