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_{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

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

Thanks for any help

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Andrew Mason

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

[tex]P_fV_f^\gamma = P_iV_i^\gamma[/tex] and

[tex]T_fV_f^{\gamma - 1} =T_iV_i^{\gamma - 1}[/tex]

where [itex]\gamma[/itex] 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

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I see! So, if the pressure increases, the temperature increases and vice-versa.This is an adiabatic expansion. So the adiabatic condition applies. If it is an ideal gas, then:

[tex]P_fV_f^\gamma = P_iV_i^\gamma[/tex] and

[tex]T_fV_f^{\gamma - 1} =T_iV_i^{\gamma - 1}[/tex]

where [itex]\gamma[/itex] is the ratio of specific heats: Cp/Cv

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?

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?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.

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Andrew Mason

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

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

AM

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