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This problem relates to the Joule-Kelvin (throttling) process discussed in Section 27.3. The Joule-Kelvin coefficient is defined according to T/p. a) For a van der Waals gas, find the inversion curve (see the dashed line in Fig. 27.3), defined to be the curve where the Joule-Kelvin coefficient is zero. Give the result in terms of the reduced variables of Problem 3, finding p' as a function of T'. You can start from Equation 27.23, and you can make use of the calculus identity: âˆ‚V/âˆ‚(ap/aT)y = (âˆ‚p/âˆ‚(ap/aV))T. This will give you a relation for V in terms of a, b, and T, which you can then substitute back into the van der Waals equation to eliminate V. After a fair amount of algebra, you can arrive at the answer p = 9 - 12T - 3. Hint: This does take a fair bit of algebra. It is a lot easier, with less writing, if you work in the reduced dimensionless variables from the start. An intermediate result is V = -1/(1 - 3T). b) Sketch a graph of the inversion curve, indicating quantitatively the intercepts on the T' axis as well as the point of maximum pressure.

Name: 5 this problem relates to the joule kelvin throttling process discussed in section 273the joule kelvin coefficient is defined according totp afor a van der waals gasfind the inversion curves 34668
Uploaded: 2023-07-25T13:16:20-08:00
Duration: 15 s
Channel: Numerade
Description: 5 this problem relates to the joule kelvin throttling process discussed in section 273the joule kelvin coefficient is defined according totp afor a van der waals gasfind the inversion curves 34668

          This problem relates to the Joule-Kelvin (throttling) process discussed in Section 27.3. The Joule-Kelvin coefficient is defined according to T/p.

a) For a van der Waals gas, find the inversion curve (see the dashed line in Fig. 27.3), defined to be the curve where the Joule-Kelvin coefficient is zero. Give the result in terms of the reduced variables of Problem 3, finding p' as a function of T'. You can start from Equation 27.23, and you can make use of the calculus identity: âˆ‚V/âˆ‚(ap/aT)y = (âˆ‚p/âˆ‚(ap/aV))T. This will give you a relation for V in terms of a, b, and T, which you can then substitute back into the van der Waals equation to eliminate V. After a fair amount of algebra, you can arrive at the answer p = 9 - 12T - 3. Hint: This does take a fair bit of algebra. It is a lot easier, with less writing, if you work in the reduced dimensionless variables from the start. An intermediate result is V = -1/(1 - 3T).

b) Sketch a graph of the inversion curve, indicating quantitatively the intercepts on the T' axis as well as the point of maximum pressure.

5 this problem relates to the joule kelvin throttling process discussed in section 273the joule kelvin coefficient is defined according totp afor a van der waals gasfind the inversion curves 34668

Added by Mario E.

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