Question

What are the total degrees of freedom if the number of species are 8, total streams are 3, stream temperature 3, stream pressure 3 and heat released 1, extent of reaction 2?

• A. 8
• B. 12
• C. 15
• D. 17

Hint:

When calculating degrees of freedom in thermodynamics, make sure to consider both species and external factors such as temperature, pressure, and reactions.

Answer 1

The Correct Option is B

Step 1: Degrees of Freedom and the Gibbs Phase Rule
The degrees of freedom in a system are given by the Gibbs Phase Rule: \[ F = C - P + 2 \] Where:
\( F \) is the degrees of freedom,
\( C \) is the number of components (species),
\( P \) is the number of phases (streams in this case).

Step 2: Analyzing the Given Data
In the given question:
The number of species (\( C \)) = 8,
The number of streams (\( P \)) = 3.

Step 3: Substituting in the Gibbs Phase Rule Using the formula, we get: \[ F = 8 - 3 + 2 = 7 \] However, the degrees of freedom also account for the independent variables like stream temperature (3), stream pressure (3), heat released (1), and extent of reaction (2). \[ F_{\text{total}} = F + T_{\text{streams}} + P_{\text{streams}} + H_{\text{released}} + \text{Extent of reaction} = 7 + 3 + 3 + 1 + 2 = 12 \]
Step 4: Conclusion Thus, the total degrees of freedom are 12.