What happens as a gas expands?

[YMMMA]

Homework Statement

In the figure below, the volume expands while the pressure is constant. What happens when this gas expands?
A) heat is added and temperature increased
B) heat is removed and temperature decreasesd
C) heat is added and temperature decreased
D) heat is removed and temperature increased
E) heat is removed and temperature stays constant.

Homework Equations

First law of thermodynamicsm ΔU=Q-W

Ideal Gas Law: PV=nRT

The Attempt at a Solution

Well, as the volume increases, pressure stays the same, and the temperature also increases. Here, work is done by the gas to expand the system. So, work is positive, ΔU=Q-(+W). And since temperature increased, so does the change in internal energy of the system. Therefore, heat is added to the system.

Is my reasoning correct? That topic confuses me sometimes, so I need someone to check on my understanding. Work is done on the gas ΔU=Q-(-W). Work is done by the gas ΔU=Q-(+W). To know the temperature or the change in internal energy, use the ideal gas law. And heat depends on both of these factors, change in internal energy and work, so I can know whether heat is added or removed by knowing them.

 

[ehild]

Homework Statement

In the figure below, the volume expands while the pressure is constant. What happens when this gas expands?
A) heat is added and temperature increased
B) heat is removed and temperature decreasesd
C) heat is added and temperature decreased
D) heat is removed and temperature increased
E) heat is removed and temperature stays constant.

Homework Equations

First law of thermodynamicsm ΔU=Q-W

Ideal Gas Law: PV=nRT

The Attempt at a Solution

Well, as the volume increases, pressure stays the same, and the temperature also increases. Here, work is done by the gas to expand the system. So, work is positive, ΔU=Q-(+W). And since temperature increased, so does the change in internal energy of the system. Therefore, heat is added to the system.

Is my reasoning correct? That topic confuses me sometimes, so I need someone to check on my understanding. Work is done on the gas ΔU=Q-(-W). Work is done by the gas ΔU=Q-(+W). To know the temperature or the change in internal energy, use the ideal gas law. And heat depends on both of these factors, change in internal energy and work, so I can know whether heat is added or removed by knowing them.

Your reasoning is correct. You even can determine the heat added to an ideal gas. What is the internal energy in terms of temperature? Knowing the pressure and change of volume you can determine the work done by the gas. From the first law, you can determine the heat added.

 

[YMMMA]

Thank you!

Your reasoning is correct. You even can determine the heat added to an ideal gas. What is the internal energy in terms of temperature? Knowing the pressure and change of volume you can determine the work done by the gas. From the first law, you can determine the heat added.

 

[HenryE]

If the volume increases, the only two ways pressure could remain constant are by adding more gas, or adding heat. Since added gas is not an option for the given problem, then added heat is responsible for maintaining the pressure.

As the volume of a gas expands, the overall temperature tends to drop because there are fewer molecules per any given volume. If properly balanced, you could supply heat for expansion at a rate that maintains a constant temperature.

For this particular problem though, the only option that fits is C.

How close am I? :)

 

[YMMMA]

As the volume of a gas expands, the overall temperature tends to drop because there are fewer molecules per any given volume. If properly balanced, you could supply heat for expansion at a rate that maintains a constant temperature.

I thought of this at first. There’s no answer key to the question, that’s why I am asking. Also, if pressure is constant and volume increased, temperature will increase as it is directly proportional to volume ( ideal gas law). Although, logically, if the volume increase while pressure is constant, there will be fewer molecules per given volume as you said. But I answered it A, anyway.

 

[ehild]

As the volume of a gas expands, the overall temperature tends to drop because there are fewer molecules per any given volume.

According to the ideal gas law PV=nRT, P=(n/V) RT, the pressure can be constant with decreasing molecular density only with increasing temperature.

 

[YMMMA]

According to the ideal gas law PV=nRT, P=(n/V) RT, the pressure can be constant with decreasing molecular density only with increasing temperature.

So, A is right?

 

[ehild]

So, A is right?

Yes.

 

[HenryE]

According to the ideal gas law PV=nRT, P=(n/V) RT, the pressure can be constant with decreasing molecular density only with increasing temperature.

LOL, I agree but think we are describing the same thing from slightly different angles. After all, isn't that what adding heat is doing? Increasing the temperature of individual gas molecules?

Even though the temperature of individual gas molecules goes up with added heat, the expansion would tend to decrease average temperature. Individual molecules would be more energetic due to their elevated temperature, but by becoming more spread out the average temperature doesn't necessarily have to increase.

I'd actually like to see an option 'F' -- Heat is added to the system but overall average temperature remains the same.

If course, a lot depends on the rate at which you can add heat to the system.

 

[ehild]

LOL, I agree but think we are describing the same thing from slightly different angles. After all, isn't that what adding heat is doing? Increasing the temperature of individual gas molecules?

No, the added heat does not increase the temperature of the gas molecules., it increase the temperature of the gas.
The temperature is related to the average translational kinetic energy of the molecules: KE_qverage=3/2 kT.
http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c1

Even though the temperature of individual gas molecules goes up with added heat, the expansion would tend to decrease average temperature. Individual molecules would be more energetic due to their elevated temperature, but by becoming more spread out the average temperature doesn't necessarily have to increase.

Average means average over the molecules, not over the volume. For the same distribution of the kinetic energy, the temperature is independent of the volume in case of an ideal gas.

I'd actually like to see an option 'F' -- Heat is added to the system but overall average temperature remains the same.

If course, a lot depends on the rate at which you can add heat to the system.

Well, consider all processes reversible, slow enough, so you can define pressure and temperature during the process. The pressure is constant. You can apply the equations PV=nRT and ΔU = Q-PΔV, and if it is an ideal gas, U=nCvT, where Cv is the specific heat at constant volume. You can determine the final temperature and added heat knowing the pressure and the initial temperature, and the initial and final volumes.

 

[HenryE]

No, the added heat does not increase the temperature of the gas molecules., it increase the temperature of the gas.
.

The gas is composed of molecules. They are one and the same. You can't increase the temperature of the gas wothout increasing the temperature of the individual molecules that constitute that gas.

Other than that, I see your point and of course have to change my answer to A, since to maintain the pressure with fewer molecules per unit of volume, they must be more energetic (hotter).

The change in volume does play a role in this particular problem though. Since the volume triples while pressure remains constant this dictates the rate at which heat can be added.

 

[ehild]

The gas is composed of molecules. They are one and the same. You can't increase the temperature of the gas wothout increasing the temperature of the individual molecules that constitute that gas.

Temperature is a macroscopic property. Molecules do not have temperature.
According to kinetic theory, the temperature of a gas is proportional to the average kinetic energy of the molecules.
The speed/kinetic energy of the individual molecules can be very different, the molecules are not the same in this regard.

 

[vela]

As the volume of a gas expands, the overall temperature tends to drop because there are fewer molecules per any given volume. If properly balanced, you could supply heat for expansion at a rate that maintains a constant temperature.

This is wrong. Suppose, for example, you have a gas confined by a barrier to half of a container, and the other half of the container is empty. If you remove the barrier, the volume of the gas will double, but the temperature of the gas won't change. As @ehild has said several times, the temperature is a measure of the average (translational) kinetic energy of the particles. It has nothing to do with the density of the gas.

In this problem, the environment exerts a pressure on the gas, so for the gas to expand, it has to do work on the surroundings. If no heat is added, the energy needed comes from the kinetic energy of the particles (at least in part), reducing their average energy and therefore lowering the temperature of the gas.