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2) In the lecture we have proved that for an ideal gas Cp,m = Cv,m + R. In the general case (i. e., not just an ideal gas) the relation between the two molar heat capacities is Cp,m = α Cv.m + where Vm = V/n is the molar volume of the substance, 10/07), V Р a² VmT K is the coefficient of thermal expansion (the derivative with respect to T is calculated keeping p constant), and K = 1 av V др T is the isothermal compressibility (the derivative with respect to pressure is calculated keeping T constant). Prove that if the substance satisfies the equation of state of an ideal gas (i. e., the substance is an ideal gas) the general relation between Cp,m and Cv,m reduces to the simple ideal gas relation Cp,m = Cv,m + R.

2) In the lecture we have proved that for an ideal gas Cp,m = Cv,m + R. In the general case (i. e., not just an ideal gas) the relation between the two molar heat capacities is Cp,m = α Cv.m + where Vm = V/n is the molar volume of the substance, 10/07), V Р a² VmT K is the coefficient of thermal expansion (the derivative with respect to T is calculated keeping p constant), and K = 1 av V др T is the isothermal compressibility (the derivative with respect to pressure is calculated keeping T constant). Prove that if the substance satisfies the equation of state of an ideal gas (i. e., the substance is an ideal gas) the general relation between Cp,m and Cv,m reduces to the simple ideal gas relation Cp,m = Cv,m + R.

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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2) In the lecture we have proved that for an ideal gas Cp,m = Cv.m + R. In the general case (i. e., not just an ideal gas) the relation between the two molar heat capacities is Cp,m = Cv.m + where Vm = V/n is the molar volume of the substance, 1 av V ƏT α = a² VmT K K = is the coefficient of thermal expansion (the derivative with respect to T is calculated keeping p constant), and P 1 ᎧᏙ у др/ т is the isothermal compressibility (the derivative with respect to pressure is calculated keeping T constant). Prove that if the substance satisfies the equation of state of an ideal gas (i. e., the substance is an ideal gas) the general relation between Cp,m and Cv,m reduces to the simple ideal gas relation Cp,m Cv.m + R. - =
Transcribed Image Text:2) In the lecture we have proved that for an ideal gas Cp,m = Cv.m + R. In the general case (i. e., not just an ideal gas) the relation between the two molar heat capacities is Cp,m = Cv.m + where Vm = V/n is the molar volume of the substance, 1 av V ƏT α = a² VmT K K = is the coefficient of thermal expansion (the derivative with respect to T is calculated keeping p constant), and P 1 ᎧᏙ у др/ т is the isothermal compressibility (the derivative with respect to pressure is calculated keeping T constant). Prove that if the substance satisfies the equation of state of an ideal gas (i. e., the substance is an ideal gas) the general relation between Cp,m and Cv,m reduces to the simple ideal gas relation Cp,m Cv.m + R. - =
Expert Solution
Given

Given that, the relation between two molar heat capacities is

Cp,m = CV, m + α2VmTκ, where Vm = Vn.

Where, α is the coefficient of thermal expansion, α = 1V∂V∂Tp,

and β is the thermal compressibility, β = -1V∂V∂pT.

We have to prove that for an ideal gas Cp,m = CV, m + R.

Introduction: The ideal gas equation is pV = nRT.

 

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