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Medgen

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I'm working through the EK 1001 Chemistry, and am a little confused by a few of their solutions. In two of their solutions they indicate quite explicitly that the work done in a free adiabatic expansion of a gas is zero and that the temperature of an ideal gas undergoing a free adiabatic expansion remains constant.

But I thought that in an adiabatic expansion, you could still have pressure volume expansion doing work and thus a change in internal energy and a change in temperature... You just can't have any heat. Am I missing something or is EK wrong?
 

Axon hillock

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I'm working through the EK 1001 Chemistry, and am a little confused by a few of their solutions. In two of their solutions they indicate quite explicitly that the work done in a free adiabatic expansion of a gas is zero and that the temperature of an ideal gas undergoing a free adiabatic expansion remains constant.

But I thought that in an adiabatic expansion, you could still have pressure volume expansion doing work and thus a change in internal energy and a change in temperature... You just can't have any heat. Am I missing something or is EK wrong?

Usually adiabatic expansion means that there is still PV work being done. However, in your case the question said the gas was undergoing free adibatic expansion which is a special case. No work is done by the gas and the temperature doesn't change because the volume is constant. It's a tricky question.
 

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The adiabatic free expansion is an important model transformation for thermodynamics. In a normal adiabatic expansion, such as with an insulated piston, the PV work done by the gas is reflected in a decreased temperature. With the adiabatic free expansion, the final state is equivalent to an isothermal expansion.

This is a 1st law question, but in teaching the adiabatic free expansion is an important model for entropy change where no heat flow occurs. Because the entropy is a state function, you can derive the entropy change in the free expansion using the heat flow from the isothermal transformation which would bring the system from the same initial to final state. However, because the heat flowing into an isothermally expanding system is equaled by heat flowing out of the surroundings, the entropy of the universe doesn't change, even though the entropy of the system has increased. With the adiabatic free expansion, there is no compensating decrease in entropy with the surroundings, so entropy in the universe increases. For this reason, even though the isothermal expansion and the adiabatic free expansion have the same initial and final states, and the same entropy change within the system, the isothermal expansion is reversible while the adiabatic free expansion is not.
 

fallingwater

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I'm having trouble with the same EK questions. Is no work done in a free adiabatic expansion because there can be no accompanying heat exchange with the environment? Or is it simply no work done because PV remains constant?
 

whiteshadodw

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I'm having trouble with the same EK questions. Is no work done in a free adiabatic expansion because there can be no accompanying heat exchange with the environment? Or is it simply no work done because PV remains constant?

in free adiabatic expansion in a container there is apparently a vacuum allowing the gas to expand and because the volume of the container doesn't change then PV doesn't change and no work is done. however, since the gas has expanded the gas does increase in entropy despite the fact that temperature has remained the same (TdS only applies in reversible situations, i think free adiabatic expansion is irreversible).

to be quite honest though, most of this stuff goes beyond the scope of the MCAT and if it does show up then expect a thorough explanation of what is going on.
 

fallingwater

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Thanks for your reply! EK says that pressure does change during a free adiabatic expansion in a container. So to determine if work is done, should only the quantity PdV be considered (which doesn't change), and not PV (which does change, since pressure but not volume changes)?
 

zwander

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But I mean you could still say work is being done, although not PV work. THe thing you described is analogous to the flow of H+ ions into the mitochondrial matrix (secondary active transport) which provides enough energy (supplies work) to couple the formation of ATP. Right?

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The adiabatic free expansion is an important model transformation for thermodynamics. In a normal adiabatic expansion, such as with an insulated piston, the PV work done by the gas is reflected in a decreased temperature. With the adiabatic free expansion, the final state is equivalent to an isothermal expansion.

This is a 1st law question, but in teaching the adiabatic free expansion is an important model for entropy change where no heat flow occurs. Because the entropy is a state function, you can derive the entropy change in the free expansion using the heat flow from the isothermal transformation which would bring the system from the same initial to final state. However, because the heat flowing into an isothermally expanding system is equaled by heat flowing out of the surroundings, the entropy of the universe doesn't change, even though the entropy of the system has increased. With the adiabatic free expansion, there is no compensating decrease in entropy with the surroundings, so entropy in the universe increases. For this reason, even though the isothermal expansion and the adiabatic free expansion have the same initial and final states, and the same entropy change within the system, the isothermal expansion is reversible while the adiabatic free expansion is not.
 
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