Partial Derivatives Applied to Chemistry

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SUMMARY

The discussion focuses on applying partial derivatives in chemistry, specifically using the chain rule and cyclic rule in the context of the equation dp/dv = d(nRT/V)/dV. Participants emphasize the importance of holding variables n (number of moles) and T (temperature) constant while differentiating. The conversation highlights the confusion surrounding the cyclic rule and clarifies that the chain rule is the appropriate method for this problem.

PREREQUISITES
  • Understanding of partial derivatives in calculus
  • Familiarity with the chain rule in differentiation
  • Basic knowledge of thermodynamic equations, specifically the ideal gas law
  • Concept of holding variables constant in mathematical equations
NEXT STEPS
  • Study the application of the chain rule in multivariable calculus
  • Explore the cyclic rule and its applications in thermodynamics
  • Review the ideal gas law and its implications in chemistry
  • Practice problems involving partial derivatives in physical chemistry contexts
USEFUL FOR

Chemistry students, educators, and anyone studying thermodynamics or multivariable calculus who seeks to understand the application of partial derivatives in chemical equations.

ramsharmjarm
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Homework Statement


Please look at the attached pic. I don't know how to type all these symbols in.


Homework Equations



Im not sure how to start

The Attempt at a Solution



I tried using the cyclic rule but the problem just started getting messier.
 

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I don't know what you mean by the "cylic rule" but this is a simple application of the "chain rule". Of course, the fact that n and T are held constant is important.
 
am i starting this right then?

dp/dv = d(nRT/V)/dV= dnrT/Vdv)
 

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