Why Change Total Derivative to Partial in dU=TdS-PdV?

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Homework Help Overview

The discussion revolves around the thermodynamic equation dU=TdS-PdV and the reasoning behind changing the total derivative to a partial derivative in this context.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the conditions under which the total derivative can be expressed as a partial derivative, particularly focusing on the implications of holding certain variables constant.

Discussion Status

Some participants have provided insights into the reasoning behind the use of partial derivatives, while others have expressed gratitude for the clarification. Multiple interpretations of the equation and its components are being explored.

Contextual Notes

There is an emphasis on the conditions of the variables involved, specifically the treatment of volume as a constant during differentiation.

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for the equation:
dU=TdS-PdV
why can you can the total derivative to a partial derivative, which makes the equation become
T=(partial derivative U)/(particle derivative S) ?
 
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You are taking the partial derivative of U with respect to S with V held fixed. So you take dV=0, and then divide through by dS.
 
Because dU is an integrable differential one-form.

Daniel.
 
thank you very much! :)
 

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