Thermodynamics and Gas Laws

[uestions]

There is a container of a fixed volume filled with gas. There is a second container with a piston filled with gas. The containers are filled with the same amount of gas, have the same pressure, have the same volume (the piston is placed so the gases of each container occupy the same volume), and are at the same temperature.
I add equal amounts of heat to each container. The fixed-volume container increases in temperature; the piston of the second container is pushed out and the gas also increases in temperature.
Since the gas in the piston-container does work, does that mean its temperature is less than that of the constant-volume container? I would assume so because the added heat is transferred away as work.
Also, how does the relationship between V and T take into account the energy lost, and therefore decrease in temperature, when an expanding gas does work?

 

[Chestermiller]

There is a container of a fixed volume filled with gas. There is a second container with a piston filled with gas. The containers are filled with the same amount of gas, have the same pressure, have the same volume (the piston is placed so the gases of each container occupy the same volume), and are at the same temperature.
I add equal amounts of heat to each container. The fixed-volume container increases in temperature; the piston of the second container is pushed out and the gas also increases in temperature.
Since the gas in the piston-container does work, does that mean its temperature is less than that of the constant-volume container? I would assume so because the added heat is transferred away as work.

Yes.

Also, how does the relationship between V and T take into account the energy lost, and therefore decrease in temperature, when an expanding gas does work?

The relationship between V and T doesn't focus on the energy lost. The energy lost is accounted for by the First Law of Thermodynamics, which is essentially an energy balance:

ΔU = Q - W

where Q is the amount of heat absorbed from the surroundings, W is the amount of work done on the surroundings, and U is the internal energy of the gas. For an ideal gas, the internal energy is a monotonically increasing function of temperature.

Chet

 

[uestions]

Can a gas expand and lose temperature (because it did work on a piston while expanding)?

 

[Chestermiller]

Can a gas expand and lose temperature (because it did work on a piston while expanding)?

Yes.

 

[LudusRex]

I can confirm that the laws of thermodynamics and gas laws play a crucial role in understanding the behavior of gases in different containers. In this scenario, we have two containers of equal volume, pressure, and temperature, filled with the same amount of gas. When equal amounts of heat are added to both containers, the gas in the fixed-volume container increases in temperature, while the gas in the piston-container expands and also increases in temperature.

The reason for this is because the gas in the fixed-volume container cannot do any work, as it is confined to a fixed volume. Therefore, all the added heat is converted into internal energy, leading to an increase in temperature. On the other hand, the gas in the piston-container can do work as it expands against the external pressure of the piston. This work done by the gas results in a decrease in its internal energy, causing a decrease in temperature.

To answer your question, the temperature of the gas in the piston-container will indeed be lower than that of the gas in the fixed-volume container. This is because the added heat is not only used to increase the internal energy of the gas, but also to do work, resulting in a decrease in temperature.

The relationship between volume and temperature, known as the Charles's Law, states that at a constant pressure, the volume of a gas is directly proportional to its temperature. However, in this scenario, the expanding gas does work, and therefore, the relationship between volume and temperature may not be a direct one. The exact relationship would depend on the amount of work done by the gas and the heat added to the system.

In conclusion, the behavior of gases in different containers is governed by the laws of thermodynamics and gas laws, and the work done by the gas plays a crucial role in determining its temperature and other properties.