Explanation Write the given equation of state of gas. v = R T P − a T + b (I) Here, the pressure is P , the specific volume is v , the universal gas constant is R , the temperature is T and the constants are a and b . Refer Equation (12-52). Write the general relation for Joule-Thomson coefficient. μ JT = ( ∂ T ∂ P ) h = − 1 c P [ v − T ( ∂ v ∂ T ) P ] = 1 c P [ T ( ∂ v ∂ T ) P − v ] (II) Here, the Joule-Thomson coefficient is μ JT , the temperature is T , the pressure is P , the enthalpy is h , the specific heat at constant pressure is c P and the change of specific volume with respect to temperature at constant pressure is ( ∂ v ∂ T ) P . Conclusion: Partially differentiate the Equation (I) with respect to the temperature ( T ) by keeping the pressure ( P ) as constant. ( ∂ v ∂ T ) P = ∂ ∂ T ( R T P − a T + b ) = ∂ ∂ T ( R T P ) − ∂ ∂ T ( a T ) + ∂ ∂ T ( b ) = R P ( 1 ) − a ( − 1 T 2 ) + 0 = R P + a T 2 When, the Joule-Thomson coefficient is zero

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Chapter 12.6, Problem 66P

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To derive an equation for the Joule-Thomson coefficient inversion line.

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Chapter 12.6, Problem 65P

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To derive an equation for the Joule-Thomson coefficient inversion line.

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