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A plane surface having an area of 1.0 m² is insulated on the bottom side and is placed on the ground exposed to the atmosphere at night. The upper surface is exposed to air at 290 K, and the convection heat transfer coefficient between the air and surface is 12 W/m²-K. The surface also radiates to the clear sky, and the effective radiation temperature of the sky can be assumed to be 80 K. If the plane surface is assumed to be a black body, calculate the equilibrium temperature of the surface. Note: the temperature of the plane surface is less than the air temperature.

A plane surface having an area of 1.0 m² is insulated on the bottom side and is placed on the ground exposed to the atmosphere at night. The upper surface is exposed to air at 290 K, and the convection heat transfer coefficient between the air and surface is 12 W/m²-K. The surface also radiates to the clear sky, and the effective radiation temperature of the sky can be assumed to be 80 K. If the plane surface is assumed to be a black body, calculate the equilibrium temperature of the surface. Note: the temperature of the plane surface is less than the air temperature.

Introduction to Chemical Engineering Thermodynamics
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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**Problem Statement:** A plane surface having an area of 1.0 m² is insulated on the bottom side and is placed on the ground, exposed to the atmosphere at night. The upper surface is exposed to air at 290 K, and the convection heat transfer coefficient between the air and surface is 12 W/m²·K. The surface also radiates to the clear sky, and the effective radiation temperature of the sky can be assumed to be 80 K. If the plane surface is assumed to be a black body, calculate the equilibrium temperature of the surface. Note: the temperature of the plane surface is less than the air temperature. --- **Explanation:** - **Surface Area**: The exposed surface has an area of 1.0 m². - **Insulation**: The bottom side is insulated, meaning no heat transfer occurs from this side. - **Air Exposure**: The upper surface is exposed to air at a temperature of 290 K. - **Convection**: A convection heat transfer occurs between the air and the surface with a coefficient of 12 W/m²·K. - **Radiation**: The surface radiates energy to the sky, with the sky's effective radiation temperature assumed to be 80 K. - **Black Body Assumption**: The surface is assumed to be a perfect black body, meaning it absorbs and emits radiation perfectly. **Objective**: Calculate the equilibrium temperature of the surface, which will be less than the air temperature of 290 K.
Transcribed Image Text:**Problem Statement:** A plane surface having an area of 1.0 m² is insulated on the bottom side and is placed on the ground, exposed to the atmosphere at night. The upper surface is exposed to air at 290 K, and the convection heat transfer coefficient between the air and surface is 12 W/m²·K. The surface also radiates to the clear sky, and the effective radiation temperature of the sky can be assumed to be 80 K. If the plane surface is assumed to be a black body, calculate the equilibrium temperature of the surface. Note: the temperature of the plane surface is less than the air temperature. --- **Explanation:** - **Surface Area**: The exposed surface has an area of 1.0 m². - **Insulation**: The bottom side is insulated, meaning no heat transfer occurs from this side. - **Air Exposure**: The upper surface is exposed to air at a temperature of 290 K. - **Convection**: A convection heat transfer occurs between the air and the surface with a coefficient of 12 W/m²·K. - **Radiation**: The surface radiates energy to the sky, with the sky's effective radiation temperature assumed to be 80 K. - **Black Body Assumption**: The surface is assumed to be a perfect black body, meaning it absorbs and emits radiation perfectly. **Objective**: Calculate the equilibrium temperature of the surface, which will be less than the air temperature of 290 K.
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