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# Differences

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activities:guides:eembpdmlegendretransforms 2018/11/15 08:49 | activities:guides:eembpdmlegendretransforms 2018/11/15 08:52 current | ||
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==== Activity: Wrap-up ==== | ==== Activity: Wrap-up ==== | ||

- | * Internal energy keeps track of the work (and heat) that goes into and out of a system. These other energies keep track of the energy that goes into or out of the system in other ways (than heat and work). For example, $\Delta A = F_L\Delta x_R-x_R\Delta F_R$ takes into account work on the left side of the PDM but some other form of energy exchange on the right side (for which we have no name). $A$ is a state variable that we can write in terms of other state variables ($A=U-F_Rx_R \implies dA=dU-F_Rdx_R-x_RdF_R$), which is a statement known as a Legendre transformation. | + | * Internal energy keeps track of the work (and heat) that goes into and out of a system. These other energies keep track of the energy that goes into or out of the system in other ways (than heat and work). For example, $\Delta A = F_L\Delta x_L-x_R\Delta F_R$ takes into account work on the left side of the PDM but some other form of energy exchange on the right side (for which we have no name). $A$ is a state variable that we can write in terms of other state variables ($A=U-F_Rx_R \implies dA=dU-F_Rdx_R-x_RdF_R$), which is a statement known as a Legendre transformation. |

- | * It is not always easy to come up with a physical rationalization of these other energies, though it becomes easier if one state variable remains constant throughout a process. For example, if $F_R$ is constant, then $\Delta A = F_L\Delta x_R = \Delta U - F_RdX_R$ | + | * It is not always easy to come up with a physical rationalization of these other energies, though it becomes easier if one state variable remains constant throughout a process. For example, if $F_R$ is constant, then $\Delta A = F_L\Delta x_L = \Delta U - F_R\Delta x_R$, and thus $\Delta A$ can be interpreted as the change in internal energy minus the work that the system does on the **constant** mass on the right. |

+ | /*BEGIN COMMENT | ||

Physically interpret $F_Lx_L$ and $F_Rx_R$ as potential energies, though emphasize that such interpretations in thermodynamics are not always possible. | Physically interpret $F_Lx_L$ and $F_Rx_R$ as potential energies, though emphasize that such interpretations in thermodynamics are not always possible. | ||

- | /*BEGIN COMMENT | ||

Once groups have had enough time to find the requested partial derivative(s), convene the class. Ask (to the class) a group to describe how they went about finding the requested partial derivative. Once a group reports their process, ask (to the class) the other groups if they used the same process. If there are other processes, ask for groups to justify their process. If this does not result in a unanimous agreement upon a correct process(es), describe each correct process to the class and expose the errors in any incorrect process that was used. Repeat this for every requested partial derivative. | Once groups have had enough time to find the requested partial derivative(s), convene the class. Ask (to the class) a group to describe how they went about finding the requested partial derivative. Once a group reports their process, ask (to the class) the other groups if they used the same process. If there are other processes, ask for groups to justify their process. If this does not result in a unanimous agreement upon a correct process(es), describe each correct process to the class and expose the errors in any incorrect process that was used. Repeat this for every requested partial derivative. | ||

END COMMENT */ | END COMMENT */ |