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An iron bar 2 cm x 3 cm x 10 cm at a temperature of 95°C is dropped into a barrel of water at 25°C. The barrel is large enough that the water temperature rises negligibly as the bar cools. The rate at which heat is transferred from the bar to the water is given by Q(J/min) = UA(Tb - Tw) where U (= 0.050 J/min cm² °C) is a heat-transfer coefficient, A (cm²) is the exposed area of the bar, T, is the surface temperature of the bar, and Tw is the water temperature. Given that the heat capacity of the bar is 0.460 J/g °C, and heat conduction in iron is fast enough to assume that the temperature Tu(t) is uniform throughout the bar, write an energy balance on the bar and determine the steady state temperature of the bar. Also, calculate the time required for the bar to cool to 30°C.

An iron bar 2 cm x 3 cm x 10 cm at a temperature of 95°C is dropped into a barrel of water at 25°C. The barrel is large enough that the water temperature rises negligibly as the bar cools. The rate at which heat is transferred from the bar to the water is given by Q(J/min) = UA(Tb - Tw) where U (= 0.050 J/min cm² °C) is a heat-transfer coefficient, A (cm²) is the exposed area of the bar, T, is the surface temperature of the bar, and Tw is the water temperature. Given that the heat capacity of the bar is 0.460 J/g °C, and heat conduction in iron is fast enough to assume that the temperature Tu(t) is uniform throughout the bar, write an energy balance on the bar and determine the steady state temperature of the bar. Also, calculate the time required for the bar to cool to 30°C.

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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H.W.1 An iron bar 2 cm x 3 cm x 10 cm at a temperature of 95°C is dropped into a barrel of water at 25°C. The barrel is large enough that the water temperature rises negligibly as the bar cools. The rate at which heat is transferred from the bar to the water is given by Q(J/min) = UA(Tb - Tw) where U (= 0.050 J/min cm² °C) is a heat-transfer coefficient, A (cm²) is the exposed area of the bar, T, is the surface temperature of the bar, and Tw is the water temperature. Given that the heat capacity of the bar is 0.460 J/g °C, and heat conduction in iron is fast enough to assume that the temperature Th() is uniform throughout the bar, write an energy balance on the bar and determine the steady state temperature of the bar. Also, calculate the time required for the bar to cool to 30°C.
Transcribed Image Text:H.W.1 An iron bar 2 cm x 3 cm x 10 cm at a temperature of 95°C is dropped into a barrel of water at 25°C. The barrel is large enough that the water temperature rises negligibly as the bar cools. The rate at which heat is transferred from the bar to the water is given by Q(J/min) = UA(Tb - Tw) where U (= 0.050 J/min cm² °C) is a heat-transfer coefficient, A (cm²) is the exposed area of the bar, T, is the surface temperature of the bar, and Tw is the water temperature. Given that the heat capacity of the bar is 0.460 J/g °C, and heat conduction in iron is fast enough to assume that the temperature Th() is uniform throughout the bar, write an energy balance on the bar and determine the steady state temperature of the bar. Also, calculate the time required for the bar to cool to 30°C.
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