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    Solution For Chapter 16. Temperature and Heat

    Uploaded by

    nomio12
    This document contains solutions to multiple physics problems involving heat transfer and temperature change. Problem 46 calculates the time needed to raise the temperature of a large lake by 10°C when receiving a constant rate of incident solar energy. Problem 51 finds the maximum mass of water that can be heated to a certain temperature by two heat sources operating at different power levels. Problem 65 determines the equilibrium temperature reached when a hot iron object cools by transferring heat to cooler water until they equalize in temperature. Problems 76 and 80 solve heat transfer differential equations to determine heat flow rates through cylindrical and conical objects with varying radii and temperatures across their surfaces.

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    Solution For Chapter 16. Temperature and Heat

    Uploaded by

    nomio12
    28 views2 pages
    This document contains solutions to multiple physics problems involving heat transfer and temperature change. Problem 46 calculates the time needed to raise the temperature of a large lake by 10°C when receiving a constant rate of incident solar energy. Problem 51 finds the maximum mass of water that can be heated to a certain temperature by two heat sources operating at different power levels. Problem 65 determines the equilibrium temperature reached when a hot iron object cools by transferring heat to cooler water until they equalize in temperature. Problems 76 and 80 solve heat transfer differential equations to determine heat flow rates through cylindrical and conical objects with varying radii and temperatures across their surfaces.

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    Ch 16. ├▀├╡╣«┴ª - Copy.pdf

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    This document contains solutions to multiple physics problems involving heat transfer and temperature change. Problem 46 calculates the time needed to raise the temperature of a large lake by 10°C when receiving a constant rate of incident solar energy. Problem 51 finds the maximum mass of water that can be heated to a certain temperature by two heat sources operating at different power levels. Problem 65 determines the equilibrium temperature reached when a hot iron object cools by transferring heat to cooler water until they equalize in temperature. Problems 76 and 80 solve heat transfer differential equations to determine heat flow rates through cylindrical and conical objects with varying radii and temperatures across their surfaces.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    28 views2 pages

    Solution For Chapter 16. Temperature and Heat

    Uploaded by

    nomio12
    This document contains solutions to multiple physics problems involving heat transfer and temperature change. Problem 46 calculates the time needed to raise the temperature of a large lake by 10°C when receiving a constant rate of incident solar energy. Problem 51 finds the maximum mass of water that can be heated to a certain temperature by two heat sources operating at different power levels. Problem 65 determines the equilibrium temperature reached when a hot iron object cools by transferring heat to cooler water until they equalize in temperature. Problems 76 and 80 solve heat transfer differential equations to determine heat flow rates through cylindrical and conical objects with varying radii and temperatures across their surfaces.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Solution for Chapter 16.

    Temperature and Heat

    46.

    Incident energy should be same with the energy to increase the temperature of the
    lake.
    200W/m2 (103 m)2 (time)

    = (20 C 10 C) 4184J/kg K (103 m)2 10m 1g/cm3 106 cm3 /m3

    (time) = 2.092 109 s 24213 days

    51.

    Mass of the water : m[kg]


    4.184kJ/kgK m+1.1kJ/K 4.184kJ/kgKm
    1600W
    (Tf Ti ) 675W
    (Tf Ti )

    m 1.92 101 kg

    65.

    Equilibrium temperature : T [ C]
    Energy lost from the iron should be same with the energy to increase the temperature
    of the water.
    (550 C T ) 1.1kg 447J/kg K = (T 20 C) 15kg 4184J/kg K

    T = 24.12 C

    76.

    Heat would flow from the side of the cylinder. Lets consider a hollow cylinder with
    length L, radius r, and infinitesimal thickness dr, as described in the figure. Then the
    area of the side is given by 2rL.
    H = kA dT
    dr
    = k(2rL) dT
    dr

    Since r is the only variable in here; the others are constants, the differential equation
    can be easily solved by separation of variable.
    H 1r dr = 2kLdT
    R R2 R T2
    R1
    H 1r dr = 2kL T1
    dT

    H ln(R2 /R1 ) = 2kL(T1 T2 )


    2kL(T1 T2 )
    H = ln(R2 /R1 )

    1
    80.

    Unlike the problem 76, in this problem, the heat flows through the bottom and top
    of the truncated cone. Imagine a disk with radius r(R1 < r < R2 ), and infinitesimal
    thickness dl. Then the heat flow is given as following.

    H = k(r2 ) dT
    dl

    However, there is a relation between r and l which can be obtained from the proportion
    relation.
    L
    l(r) = R2 R1
    r

    Then the heat flow can written as,

    H = k(r2 ) R2 R
    L
    1 dT
    dr

    Similar to problem 76, this can be solved using separation of varialbes.


    L
    R R2 1 R T2
    H R2 R R r 2 dr = k T dT
    1 1 1

    L
    H R2 R 1
    ( R12 + 1
    R1
    ) = k(T1 T2 )

    H = kR1 R2 (T1 T2 )/L

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