How Does Temperature Change When Gas Expands in an Insulated System?

[Dassinia]

Hello,
I just have a question.
When a gaz expands against a piston (that is insulated), the system is doing work so W>0 and we know that the volume will increase and the pressure decrease.

But what I want to know, is how about the temperature, I'd say that it will decrease since the pressure also decreases , but is there any other argument ?

I know that if we want to maintain a constant temperature in such a system we have to "connect" the system to a tank , so that the heat transfer will compensate the work done by the system.

Thanks !

 

[vela]

As you noted, a pressure decrease can occur while the temperature remains constant, so saying decreasing pressure implies decreasing temperature isn't a good argument. Think instead about what happens to the internal energy of the gas if Q=0 and W>0.

 

[Dassinia]

We have that dE=-W
Ef-Ei = -W <0
We must have Ef<Ei that means that the kinetic energy in the final state is <
So the temperature decreases

 

[vela]

Yup.

 

[HalfLostAndSearching]

Hello, thank you for your question. When a gas expands against a piston in an insulated system, the work done by the gas is positive and the volume increases while the pressure decreases. This is known as an adiabatic process. In this case, the temperature of the gas will also decrease. This can be explained by the ideal gas law, which states that pressure and temperature are directly proportional when volume is held constant. Since the volume is increasing, the temperature must decrease in order to maintain a constant pressure.

Another argument for the decrease in temperature is the concept of internal energy. As the gas expands and does work against the piston, the internal energy of the gas decreases. This decrease in internal energy is reflected in a decrease in temperature.

In order to maintain a constant temperature in this system, as you mentioned, the gas would need to be connected to a heat source or sink to compensate for the work done by the gas. This would result in an isothermal process, where the temperature remains constant while the volume and pressure change.

I hope this helps answer your question. Let me know if you have any further inquiries.