Contination of problem 6 (b) part (a). What is the fugacity (bar) of CO₂ at 310 K and 8 bar? You must use the expression from Consider that at these conditions: where B'P (Bo+wB₁) Bo=0.083- B₁ 0.139- For CO₂: T= 304 K, P = 7.38 MPa, w = 0.228 0.422 T16 0.172 T4.2
Contination of problem 6 (b) part (a). What is the fugacity (bar) of CO₂ at 310 K and 8 bar? You must use the expression from Consider that at these conditions: where B'P (Bo+wB₁) Bo=0.083- B₁ 0.139- For CO₂: T= 304 K, P = 7.38 MPa, w = 0.228 0.422 T16 0.172 T4.2
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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![### Truncated Virial Equation of State
#### Problem Statement:
6. Consider the truncated virial equation of state:
\[ \frac{PV}{RT} = 1 + B'P \]
where the virial coefficient is only a function of temperature, i.e., \( B' = B'(T) \).
\( \rightarrow \) **(a) Find an expression for the fugacity coefficient using this EoS.**
The equation given is a truncated form of the virial equation of state, which provides an approximate relationship between pressure (P), volume (V), temperature (T), and the virial coefficient \( B' \) for real gases. The parameter \( B' \) is dependent on temperature and helps account for intermolecular forces and the finite volume of gas molecules.
To solve part (a), we need to derive an expression for the fugacity coefficient, which measures how much the pressure of a real gas deviates from that of an ideal gas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2802ddbc-5dac-467f-9f04-d4dff3d0fef2%2F33e01ee4-cc3a-4c42-b283-0dbc315244df%2Fbv0zj1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Truncated Virial Equation of State
#### Problem Statement:
6. Consider the truncated virial equation of state:
\[ \frac{PV}{RT} = 1 + B'P \]
where the virial coefficient is only a function of temperature, i.e., \( B' = B'(T) \).
\( \rightarrow \) **(a) Find an expression for the fugacity coefficient using this EoS.**
The equation given is a truncated form of the virial equation of state, which provides an approximate relationship between pressure (P), volume (V), temperature (T), and the virial coefficient \( B' \) for real gases. The parameter \( B' \) is dependent on temperature and helps account for intermolecular forces and the finite volume of gas molecules.
To solve part (a), we need to derive an expression for the fugacity coefficient, which measures how much the pressure of a real gas deviates from that of an ideal gas.
![### Continuation of Problem 6
**Part (b):**
**Problem Statement:**
What is the fugacity (bar) of CO₂ at 310 K and 8 bar? You must use the expression from part (a).
**Solution Approach:**
Consider the following expression under the given conditions:
\[
B'P = \frac{P_r}{T_r} \left( B_0 + \omega B_1 \right)
\]
where
\[
B_0 = 0.083 - \frac{0.422}{T_r^{1.6}}
\]
\[
B_1 = 0.139 - \frac{0.172}{T_r^{4.2}}
\]
**Given Data for CO₂:**
- \( T_c = 304 \, \text{K} \)
- \( P_c = 7.38 \, \text{MPa} \)
- \( \omega = 0.228 \)
Through this problem, students will learn to apply complex equations to determine the fugacity of gases under specified conditions, utilizing critical temperature and pressure values along with gas-specific constants. This forms part of advanced studies in thermodynamics and chemical engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2802ddbc-5dac-467f-9f04-d4dff3d0fef2%2F33e01ee4-cc3a-4c42-b283-0dbc315244df%2F8n0srta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Continuation of Problem 6
**Part (b):**
**Problem Statement:**
What is the fugacity (bar) of CO₂ at 310 K and 8 bar? You must use the expression from part (a).
**Solution Approach:**
Consider the following expression under the given conditions:
\[
B'P = \frac{P_r}{T_r} \left( B_0 + \omega B_1 \right)
\]
where
\[
B_0 = 0.083 - \frac{0.422}{T_r^{1.6}}
\]
\[
B_1 = 0.139 - \frac{0.172}{T_r^{4.2}}
\]
**Given Data for CO₂:**
- \( T_c = 304 \, \text{K} \)
- \( P_c = 7.38 \, \text{MPa} \)
- \( \omega = 0.228 \)
Through this problem, students will learn to apply complex equations to determine the fugacity of gases under specified conditions, utilizing critical temperature and pressure values along with gas-specific constants. This forms part of advanced studies in thermodynamics and chemical engineering.
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