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Demonstrate that the function P = Þp(T,V) = c1 +÷C2T² has the appropriate total differential. %3D %3D

Demonstrate that the function P = Þp(T,V) = c1 +÷C2T² has the appropriate total differential. %3D %3D

Chemistry
Chemistry
10th Edition
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
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Demonstrate that the function P = Pp (T,V) = c1-+;c,T² has the appropriate total differential.
Transcribed Image Text:Demonstrate that the function P = Pp (T,V) = c1-+;c,T² has the appropriate total differential.
Consider a particular gas. The isothermal compressibility and coefficient of thermal expansion are given by: V K = CT a ==+2V, where c, and c2 are numerical constants. T C1
Transcribed Image Text:Consider a particular gas. The isothermal compressibility and coefficient of thermal expansion are given by: V K = CT a ==+2V, where c, and c2 are numerical constants. T C1
Expert Solution
Step 1

if we calculate total differential of P as a function of Temperature and Volume with respect to isothermal compressibility factor and co-efficient of thermal expansion, then the value comes out to be 

                      c1T+c1T/V + c2T2/2

if we neglect c1T, then the given expression comes out. But we can not neglect it without any external condition. The complete solution is given in the next step. 

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