! 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

Structural Analysis
6th Edition
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Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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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.
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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