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1.34. A derivative with respect to the same variable can be taken more than once: › a/aF ax ax and is called the second derivative of F. Evaluate the following expressions, assuming the ideal gas law applies. 2²V (a) др², (b) (OP) n,T a²F ax² n,V

1.34. A derivative with respect to the same variable can be taken more than once: › a/aF ax ax and is called the second derivative of F. Evaluate the following expressions, assuming the ideal gas law applies. 2²V (a) др², (b) (OP) n,T a²F ax² n,V

Chemistry
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1.34. A derivative with respect to the same variable can be taken more than once: › a/aF ax ax and is called the second derivative of F. Evaluate the following expressions, assuming the ideal gas law applies. (355) (a) др2 n,T a²p b) (07/09) a²F ax² n,V
Transcribed Image Text:1.34. A derivative with respect to the same variable can be taken more than once: › a/aF ax ax and is called the second derivative of F. Evaluate the following expressions, assuming the ideal gas law applies. (355) (a) др2 n,T a²p b) (07/09) a²F ax² n,V
Expert Solution
Step 1: Second derivative

The given second derivative of F is fraction numerator partial differential over denominator partial differential X end fraction open parentheses fraction numerator partial differential F over denominator partial differential X end fraction close parentheses space equals space fraction numerator partial differential squared F over denominator partial differential X squared end fraction.

We have to find the expression of the below given second derivative of the following term considering the ideal gas equation.

  1. open parentheses fraction numerator partial differential squared V over denominator partial differential p squared end fraction close parentheses subscript n comma T end subscript
  2. open parentheses fraction numerator partial differential squared p over denominator partial differential T squared end fraction close parentheses subscript n comma V end subscript

Introduction: The ideal gas equation is pV = nRT.

where p is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.


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