Thermodynamics, confused with definitions

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Homework Help Overview

The discussion revolves around thermodynamic equations, specifically the relationship between internal energy (dU), heat transfer (dQ), and work done (dW). Participants are examining the implications of these equations under specific conditions, particularly at constant volume.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the equation dU = dQ + dW and its application when dW is zero. They question the validity of manipulating terms like PdV when volume is constant and discuss the implications of dV being zero.

Discussion Status

The conversation is ongoing, with participants providing insights into the conditions under which certain terms become zero. There is a focus on clarifying definitions and the implications of holding volume constant, but no consensus has been reached on the broader implications of these relationships.

Contextual Notes

Participants are navigating the definitions and conditions of thermodynamic variables, particularly in the context of homework constraints that may limit the exploration of these concepts.

Chronos000
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Homework Statement



dU = dQ + dW

so dU = Cv dT... but only if dW is zero right? as dQ = CvdT

so then the central equation is

TdS = dU + PdV

which is then TdS = CvdT + PdV according to my notes. surely PdV should be zero no?
 
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What is pdV at constant volume?
 
it is zero right?
 
yes, but why?
 
dV means change of volume, no change, dV = 0
 
my notes have further manipulated this term though, which does't seem right if its zero
 
So pdV is 0 if volume is held constant, does that mean it is always 0?

remember we may write any function of state as an exact differential, for example

dU = (\frac{\partial{U}}{\partial{S}})_{V}dS + (\frac{\partial{U}}{\partial{V}})_{s}dV

obviously at constant S one of these terms is 0, and at constant V the other is 0, but for a general change in U we need both
 

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