а. Which of these will have the largest entropy change with volume? How do you know? av T b. The Redlich-Kwong Equation RT a P = Vm - b VT Vm(Vm + b) The VdW Equation С. RT a P = Vm - b - Vm2 d. The Dieterici Equation ww ww RTe a/RTVn P = Km - b
а. Which of these will have the largest entropy change with volume? How do you know? av T b. The Redlich-Kwong Equation RT a P = Vm - b VT Vm(Vm + b) The VdW Equation С. RT a P = Vm - b - Vm2 d. The Dieterici Equation ww ww RTe a/RTVn P = Km - b
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![### Thermodynamic Equations and Entropy Change
#### a. Entropy Change with Volume
- **Question**: Which of these equations will have the largest entropy change with volume? How do you know?
- Note: This part is asking you to consider how entropy changes, particularly focusing on volume changes.
#### b. The Redlich-Kwong Equation
- **Equation**:
\[
P = \frac{RT}{V_m - b} - \frac{a}{\sqrt{T} V_m (V_m + b)}
\]
- **Explanation**: This equation is a modification of the ideal gas law that accounts for intermolecular forces and the actual volume occupied by gas molecules.
#### c. The van der Waals (VdW) Equation
- **Equation**:
\[
P = \frac{RT}{V_m - b} - \frac{a}{V_m^2}
\]
- **Explanation**: This equation further refines the ideal gas law by including terms that correct for the volume of gas particles and the intermolecular forces.
#### d. The Dieterici Equation
- **Equation**:
\[
P = \frac{RT e^{-a/RTV_m}}{V_m - b}
\]
- **Explanation**: This equation incorporates an exponential factor that accounts for molecular interaction energies, providing another approach to estimating deviations from ideal gas behavior.
### Detailed Overview
Each of these equations extends the ideal gas law to better predict the behavior of real gases by incorporating various factors that the ideal gas law does not consider:
- **Redlich-Kwong**: Introduces a temperature dependence in the correction for intermolecular forces.
- **van der Waals**: Simply adds corrections for molecular volume and forces.
- **Dieterici**: Uses an exponential term to address molecular interaction energy, considering temperature and volume interactions.
These modifications help in understanding and predicting how gases behave under different conditions, such as high pressure and low temperature, where deviations from ideality become significant. Understanding the impact of volume on entropy changes is crucial in thermodynamics and engineering applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbe75f3f-ff7d-4be4-b163-06293bfbf479%2F89af8406-3de7-45cd-965f-b0fdba53b617%2Fded4opq_processed.png&w=3840&q=75)
Transcribed Image Text:### Thermodynamic Equations and Entropy Change
#### a. Entropy Change with Volume
- **Question**: Which of these equations will have the largest entropy change with volume? How do you know?
- Note: This part is asking you to consider how entropy changes, particularly focusing on volume changes.
#### b. The Redlich-Kwong Equation
- **Equation**:
\[
P = \frac{RT}{V_m - b} - \frac{a}{\sqrt{T} V_m (V_m + b)}
\]
- **Explanation**: This equation is a modification of the ideal gas law that accounts for intermolecular forces and the actual volume occupied by gas molecules.
#### c. The van der Waals (VdW) Equation
- **Equation**:
\[
P = \frac{RT}{V_m - b} - \frac{a}{V_m^2}
\]
- **Explanation**: This equation further refines the ideal gas law by including terms that correct for the volume of gas particles and the intermolecular forces.
#### d. The Dieterici Equation
- **Equation**:
\[
P = \frac{RT e^{-a/RTV_m}}{V_m - b}
\]
- **Explanation**: This equation incorporates an exponential factor that accounts for molecular interaction energies, providing another approach to estimating deviations from ideal gas behavior.
### Detailed Overview
Each of these equations extends the ideal gas law to better predict the behavior of real gases by incorporating various factors that the ideal gas law does not consider:
- **Redlich-Kwong**: Introduces a temperature dependence in the correction for intermolecular forces.
- **van der Waals**: Simply adds corrections for molecular volume and forces.
- **Dieterici**: Uses an exponential term to address molecular interaction energy, considering temperature and volume interactions.
These modifications help in understanding and predicting how gases behave under different conditions, such as high pressure and low temperature, where deviations from ideality become significant. Understanding the impact of volume on entropy changes is crucial in thermodynamics and engineering applications.
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