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A glass window pane and a pyrex window pane are held together as shown below. Heat is flowing through the combination from the hot side to the cold side. The temperatures of the hot surface and the cold surface are shown, with the temperature of the surface between them. The glass pane has a thickness of 3.00 mm. Find the thickness of the pyrex pane. (The cross-sectional areas are not needed.) Thermal conductivity of glass kglass = 0.800 J/s m-Co Thermal conductivity of pyrex: kpyrex = 1.15 J/s•m•C°

A glass window pane and a pyrex window pane are held together as shown below. Heat is flowing through the combination from the hot side to the cold side. The temperatures of the hot surface and the cold surface are shown, with the temperature of the surface between them. The glass pane has a thickness of 3.00 mm. Find the thickness of the pyrex pane. (The cross-sectional areas are not needed.) Thermal conductivity of glass kglass = 0.800 J/s m-Co Thermal conductivity of pyrex: kpyrex = 1.15 J/s•m•C°

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Title: Heat Transfer Through a Composite Window Pane** **Introduction:** In this example, a glass window pane and a pyrex window pane are placed together to examine how heat travels through them. Heat flows from the hotter side to the colder side. The temperatures on the hot surface (\(T_1\)) and the cold surface (\(T_3\)) are given, along with the temperature at the interface (\(T_2\)). **Details:** - **Materials and Dimensions:** - **Glass Pane:** Thickness of 3.00 mm - **Pyrex Pane:** Thickness to be determined - **Thermal Conductivity Values:** - For glass, \( k_{\text{glass}} = 0.800 \, \text{J/s·m·°C} \) - For pyrex, \( k_{\text{pyrex}} = 1.15 \, \text{J/s·m·°C} \) - **Temperature Measurements:** - \( T_1 = 38^\circ \text{C} \) - \( T_2 = 23.4^\circ \text{C} \) (interface temperature) - \( T_3 = 20^\circ \text{C} \) **Diagram Explanation:** The diagram shows two solid panes in contact: 1. **Left Pane:** Labeled as "glass," with a thickness of 3.00 mm. 2. **Right Pane:** Labeled as "pyrex," with an unknown thickness represented by a question mark. Heat enters from the left side, passes through the glass, and exits through the pyrex. Three temperatures are marked: - \( T_1 = 38^\circ \text{C} \) on the left side of the glass. - \( T_2 = 23.4^\circ \text{C} \) between the glass and pyrex. - \( T_3 = 20^\circ \text{C} \) on the right side of the pyrex. **Objective:** The goal is to determine the thickness of the pyrex pane, knowing it affects the rate of heat transfer along with its thermal conductivity. Calculations would involve using the formula for heat conduction and balancing the thermal resistance across both materials. **Conclusion:** This setup offers an insightful look into conductive heat transfer across composite materials, emphasizing
Transcribed Image Text:**Title: Heat Transfer Through a Composite Window Pane** **Introduction:** In this example, a glass window pane and a pyrex window pane are placed together to examine how heat travels through them. Heat flows from the hotter side to the colder side. The temperatures on the hot surface (\(T_1\)) and the cold surface (\(T_3\)) are given, along with the temperature at the interface (\(T_2\)). **Details:** - **Materials and Dimensions:** - **Glass Pane:** Thickness of 3.00 mm - **Pyrex Pane:** Thickness to be determined - **Thermal Conductivity Values:** - For glass, \( k_{\text{glass}} = 0.800 \, \text{J/s·m·°C} \) - For pyrex, \( k_{\text{pyrex}} = 1.15 \, \text{J/s·m·°C} \) - **Temperature Measurements:** - \( T_1 = 38^\circ \text{C} \) - \( T_2 = 23.4^\circ \text{C} \) (interface temperature) - \( T_3 = 20^\circ \text{C} \) **Diagram Explanation:** The diagram shows two solid panes in contact: 1. **Left Pane:** Labeled as "glass," with a thickness of 3.00 mm. 2. **Right Pane:** Labeled as "pyrex," with an unknown thickness represented by a question mark. Heat enters from the left side, passes through the glass, and exits through the pyrex. Three temperatures are marked: - \( T_1 = 38^\circ \text{C} \) on the left side of the glass. - \( T_2 = 23.4^\circ \text{C} \) between the glass and pyrex. - \( T_3 = 20^\circ \text{C} \) on the right side of the pyrex. **Objective:** The goal is to determine the thickness of the pyrex pane, knowing it affects the rate of heat transfer along with its thermal conductivity. Calculations would involve using the formula for heat conduction and balancing the thermal resistance across both materials. **Conclusion:** This setup offers an insightful look into conductive heat transfer across composite materials, emphasizing
**Title: Thermal Radiation of Spheres in a Vacuum Chamber** **Text:** Two iron spheres with the same radius look identical from the outside, but one has a hollow cavity on the inside (see below). They are both heated to a temperature of 350°C and suspended by a thin cord from the ceiling of a vacuum chamber. The only way they can lose heat is by radiation. **Questions:** (a) Which sphere, if either, will radiate more watts of power? Explain your answer. (b) Which sphere, if either, will cool down the fastest? Explain your answer. **Diagram Explanation:** - **Diagram Overview:** - There are two iron spheres labeled **a** and **b**. - Both spheres appear identical in size and surface texture. - **Interior View:** - Sphere **a**: The interior view shows a hollow cavity inside, represented by an outer ring with an inner white circle, indicating the hollow space. - Sphere **b**: The interior view shows a completely solid structure, represented by a solid gray circle with no hollow space. This setup demonstrates how the internal structure of an object, while not visible externally, can affect its thermal properties such as heat radiation and cooling rate.
Transcribed Image Text:**Title: Thermal Radiation of Spheres in a Vacuum Chamber** **Text:** Two iron spheres with the same radius look identical from the outside, but one has a hollow cavity on the inside (see below). They are both heated to a temperature of 350°C and suspended by a thin cord from the ceiling of a vacuum chamber. The only way they can lose heat is by radiation. **Questions:** (a) Which sphere, if either, will radiate more watts of power? Explain your answer. (b) Which sphere, if either, will cool down the fastest? Explain your answer. **Diagram Explanation:** - **Diagram Overview:** - There are two iron spheres labeled **a** and **b**. - Both spheres appear identical in size and surface texture. - **Interior View:** - Sphere **a**: The interior view shows a hollow cavity inside, represented by an outer ring with an inner white circle, indicating the hollow space. - Sphere **b**: The interior view shows a completely solid structure, represented by a solid gray circle with no hollow space. This setup demonstrates how the internal structure of an object, while not visible externally, can affect its thermal properties such as heat radiation and cooling rate.
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