7.) The czpnduction heat transfer rate through a wall is modeled by the following equation: Q = k4AT L where = heat transfer rate in Btu/. /hr k = thermal conductivity of the wall A = area of the wall in ft² L = wall thickness in ft AT = steady-state temperature difference between the inside and the outside surfaces of the wall, in F° What is the appropriate unit for k if the preceding equation is to be homogeneous in units?
7.) The czpnduction heat transfer rate through a wall is modeled by the following equation: Q = k4AT L where = heat transfer rate in Btu/. /hr k = thermal conductivity of the wall A = area of the wall in ft² L = wall thickness in ft AT = steady-state temperature difference between the inside and the outside surfaces of the wall, in F° What is the appropriate unit for k if the preceding equation is to be homogeneous in units?
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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![### Conduction Heat Transfer Rate Model
The conduction heat transfer rate through a wall is modeled by the following equation:
\[
\dot{Q} = k \frac{A}{L} \Delta T
\]
**Where:**
- \(\dot{Q}\) = heat transfer rate in \(\frac{\text{Btu}}{\text{hr}}\)
- \(k\) = thermal conductivity of the wall
- \(A\) = area of the wall in \(\text{ft}^2\)
- \(L\) = wall thickness in \(\text{ft}\)
- \(\Delta T\) = steady-state temperature difference between the inside and the outside surfaces of the wall, in \(^{\circ}\text{F}\)
### Question:
What is the appropriate unit for \(k\) if the preceding equation is to be homogeneous in units?
### Explanation:
To ensure the equation is homogeneous in units, the units of \(k\) must be such that when multiplied through the expression \(\frac{A}{L} \Delta T\), the result is in \(\frac{\text{Btu}}{\text{hr}}\). This implies the units of \(k\) should compensate for the area in \(\text{ft}^2\), the thickness in \(\text{ft}\), and the temperature difference in \(^{\circ}\text{F}\). Therefore, the units for \(k\) must be \(\frac{\text{Btu}}{\text{hr} \cdot \text{ft} \cdot ^{\circ}\text{F}}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0e51a82-0555-49b1-a211-62f7b12c21bf%2F252f5797-5091-4bd6-9a59-ccf8c8ad67f9%2Fufgk47y_processed.png&w=3840&q=75)
Transcribed Image Text:### Conduction Heat Transfer Rate Model
The conduction heat transfer rate through a wall is modeled by the following equation:
\[
\dot{Q} = k \frac{A}{L} \Delta T
\]
**Where:**
- \(\dot{Q}\) = heat transfer rate in \(\frac{\text{Btu}}{\text{hr}}\)
- \(k\) = thermal conductivity of the wall
- \(A\) = area of the wall in \(\text{ft}^2\)
- \(L\) = wall thickness in \(\text{ft}\)
- \(\Delta T\) = steady-state temperature difference between the inside and the outside surfaces of the wall, in \(^{\circ}\text{F}\)
### Question:
What is the appropriate unit for \(k\) if the preceding equation is to be homogeneous in units?
### Explanation:
To ensure the equation is homogeneous in units, the units of \(k\) must be such that when multiplied through the expression \(\frac{A}{L} \Delta T\), the result is in \(\frac{\text{Btu}}{\text{hr}}\). This implies the units of \(k\) should compensate for the area in \(\text{ft}^2\), the thickness in \(\text{ft}\), and the temperature difference in \(^{\circ}\text{F}\). Therefore, the units for \(k\) must be \(\frac{\text{Btu}}{\text{hr} \cdot \text{ft} \cdot ^{\circ}\text{F}}\).
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