Derive the expressions of P, T, and vċ, in terms of (a, b) for the van der Waals equation and in terms of (A, B) for the Redlich-Kwong equation, as well as determine Z₁ = Pcvc for the van der Waals Zc RTC equation and the Redlich-Kwong equation.
Derive the expressions of P, T, and vċ, in terms of (a, b) for the van der Waals equation and in terms of (A, B) for the Redlich-Kwong equation, as well as determine Z₁ = Pcvc for the van der Waals Zc RTC equation and the Redlich-Kwong equation.
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![### Task Description
**Objective:**
Derive the expressions for critical pressure (\(P_c\)), critical temperature (\(T_c\)), and critical volume (\(v_c\)) for both the van der Waals and Redlich-Kwong equations of state.
**Parameters:**
- For the **van der Waals equation**, derive in terms of parameters \((a, b)\).
- For the **Redlich-Kwong equation**, derive in terms of parameters \((A, B)\).
**Additional Requirement:**
Calculate the critical compressibility factor \(Z_c\), defined by the equation:
\[
Z_c = \frac{P_c v_c}{R T_c}
\]
for both the van der Waals and Redlich-Kwong equations.
---
The text involves deriving expressions and understanding critical properties using these thermodynamic equations of state. The goal is to analyze and compare how these properties behave under different conditions specified by the two equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b656b52-bb2e-489d-9bef-8a32efc9339f%2F64653541-5e79-49ca-9e5f-7a558eb4f7ae%2F7di6tb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Task Description
**Objective:**
Derive the expressions for critical pressure (\(P_c\)), critical temperature (\(T_c\)), and critical volume (\(v_c\)) for both the van der Waals and Redlich-Kwong equations of state.
**Parameters:**
- For the **van der Waals equation**, derive in terms of parameters \((a, b)\).
- For the **Redlich-Kwong equation**, derive in terms of parameters \((A, B)\).
**Additional Requirement:**
Calculate the critical compressibility factor \(Z_c\), defined by the equation:
\[
Z_c = \frac{P_c v_c}{R T_c}
\]
for both the van der Waals and Redlich-Kwong equations.
---
The text involves deriving expressions and understanding critical properties using these thermodynamic equations of state. The goal is to analyze and compare how these properties behave under different conditions specified by the two equations.
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