Understanding Quasi-Static Process: Work and Temperature Changes

[spaghetti3451]

Consider a quasi-static expansion of a gas. If you change the external force by dF_ext, then the system will do work on the surroundings until the internal pressure equals the external pressure, right?

Now, how does the temperature of the system and the surroundings chnage in the process?

Thanks for any help

 

[Andrew Mason]

Consider a quasi-static expansion of a gas. If you change the external force by dF_ext, then the system will do work on the surroundings until the internal pressure equals the external pressure, right?

Now, how does the temperature of the system and the surroundings chnage in the process?

This is an adiabatic expansion. So the adiabatic condition applies. If it is an ideal gas, then:

$$P_fV_f^\gamma = P_iV_i^\gamma$$ and

$$T_fV_f^{\gamma - 1} =T_iV_i^{\gamma - 1}$$

where $\gamma$ is the ratio of specific heats: Cp/Cv

As far as the surroundings are concerned, it depends on the surroundings. Work is done on the surroundings. That may or may not change the temperature of the surroundings. For example, it might lift a weight in which case no temperature change occurrs. Or it may run a heating coil in an insulated container, in which case T increases.

AM

 

[spaghetti3451]

This is an adiabatic expansion. So the adiabatic condition applies. If it is an ideal gas, then:

$$P_fV_f^\gamma = P_iV_i^\gamma$$ and

$$T_fV_f^{\gamma - 1} =T_iV_i^{\gamma - 1}$$

where $\gamma$ is the ratio of specific heats: Cp/Cv

I see! So, if the pressure increases, the temperature increases and vice-versa.

But that's for an ideal gas only. What happens in the most general case? Is there any way to predict?

Also, is there a general adiabatic condition?

As far as the surroundings are concerned, it depends on the surroundings. Work is done on the surroundings. That may or may not change the temperature of the surroundings. For example, it might lift a weight in which case no temperature change occurrs. Or it may run a heating coil in an insulated container, in which case T increases.

I see! So you are saying that whether the temperature changes depends on the way the energy is used in the surroundings. But what if the energy is simply stored?

 

[Andrew Mason]

I see! So, if the pressure increases, the temperature increases and vice-versa.

But that's for an ideal gas only. What happens in the most general case? Is there any way to predict?

It depends on the equation of state of the gas. It will be close.

I see! So you are saying that whether the temperature changes depends on the way the energy is used in the surroundings. But what if the energy is simply stored?

If the work output is stored (say by lifting a weight) then would there be heat flow to the surroundings?

AM

 

[PJC01]

!

I can provide some insight into the understanding of quasi-static processes and the relationship between work and temperature changes. In a quasi-static expansion of a gas, the external force is changed by a small amount, dFext. This causes the system to do work on the surroundings until the internal pressure of the gas equals the external pressure.

In this process, the temperature of the system and the surroundings will both change. As the gas expands and does work on the surroundings, the internal energy of the gas decreases. This results in a decrease in temperature of the gas. At the same time, the surroundings are receiving energy from the gas through the work being done on them, causing an increase in their temperature.

The exact amount of temperature change in both the system and surroundings will depend on the specific conditions of the gas and the surroundings. However, in a quasi-static process, the changes in temperature will be small and gradual, as the system is allowed to reach equilibrium at each stage of the expansion.

It is important to note that in a quasi-static process, the changes in temperature are reversible. This means that if the external force is decreased by the same amount, the gas will contract and the temperature will return to its original value.

Overall, understanding the relationship between work and temperature changes in a quasi-static process is crucial in many scientific fields, such as thermodynamics and fluid mechanics. It allows us to predict and control the behavior of gases and other systems in various situations.