! Required information Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of R value, which has the unit of ft2-hr-°F/Btu. A certain manufacturer offers a double-pane window with R=2.5 and also a triple-pane window with R= 3.4. Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F. How much heat is lost through the double-pane window? Btu
! Required information Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of R value, which has the unit of ft2-hr-°F/Btu. A certain manufacturer offers a double-pane window with R=2.5 and also a triple-pane window with R= 3.4. Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F. How much heat is lost through the double-pane window? Btu
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter15: Computational Engineering Tools Matlab
Section: Chapter Questions
Problem 12P
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![### Required Information
Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of R value, which has the unit of ft²·hr·°F/Btu. A certain manufacturer offers a double-pane window with \( R = 2.5 \) and also a triple-pane window with \( R = 3.4 \). Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F.
#### Question:
How much heat is lost through the double-pane window?
**\[ \text{Btu} \]**
---
### Explanation:
To calculate the heat loss through a double-pane window, we need to use the formula for heat transfer through a surface with a known R value:
\[ Q = \frac{\Delta T \cdot A}{R} \]
Where:
- \( Q \) = Heat loss in Btu
- \( \Delta T \) = Temperature difference in °F
- \( A \) = Area of the window in ft²
- \( R \) = R value of the window in ft²·hr·°F/Btu
Given data for the double-pane window:
- \( \Delta T = 45°F \)
- \( R = 2.5 \) ft²·hr·°F/Btu
- \( \text{Area} = 3.5 \text{ ft} \times 5 \text{ ft} = 17.5 \text{ ft}² \)
Using the formula:
\[ Q = \frac{45 \text{ °F} \times 17.5 \text{ ft}²}{2.5 \text{ ft}²·hr·°F/Btu} \]
Step-by-step calculation:
1. Multiply the temperature difference by the area:
\[ 45 \text{ °F} \times 17.5 \text{ ft}² = 787.5 \text{ ft}²·°F \]
2. Divide by the R value:
\[ Q = \frac{787.5}{2.5} = 315 \text{ Btu/hr} \]
Thus, the heat loss through the double-pane window is 315 Btu/hr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbab71d29-f3d9-43ce-83f4-a263357daa0d%2Fd36dfd37-32e9-4cfb-bfe5-e1967d4e4f26%2Fo1f7pkk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Required Information
Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of R value, which has the unit of ft²·hr·°F/Btu. A certain manufacturer offers a double-pane window with \( R = 2.5 \) and also a triple-pane window with \( R = 3.4 \). Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F.
#### Question:
How much heat is lost through the double-pane window?
**\[ \text{Btu} \]**
---
### Explanation:
To calculate the heat loss through a double-pane window, we need to use the formula for heat transfer through a surface with a known R value:
\[ Q = \frac{\Delta T \cdot A}{R} \]
Where:
- \( Q \) = Heat loss in Btu
- \( \Delta T \) = Temperature difference in °F
- \( A \) = Area of the window in ft²
- \( R \) = R value of the window in ft²·hr·°F/Btu
Given data for the double-pane window:
- \( \Delta T = 45°F \)
- \( R = 2.5 \) ft²·hr·°F/Btu
- \( \text{Area} = 3.5 \text{ ft} \times 5 \text{ ft} = 17.5 \text{ ft}² \)
Using the formula:
\[ Q = \frac{45 \text{ °F} \times 17.5 \text{ ft}²}{2.5 \text{ ft}²·hr·°F/Btu} \]
Step-by-step calculation:
1. Multiply the temperature difference by the area:
\[ 45 \text{ °F} \times 17.5 \text{ ft}² = 787.5 \text{ ft}²·°F \]
2. Divide by the R value:
\[ Q = \frac{787.5}{2.5} = 315 \text{ Btu/hr} \]
Thus, the heat loss through the double-pane window is 315 Btu/hr.
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