A 400 g block of ice at 0 C is placed inside an empty copper bowl at 30 C”. Given enough time, this system reaches a steady state temperatur

Question

A 400 g block of ice at 0 C is placed inside an empty copper bowl at 30 C”. Given enough time, this system reaches a steady state temperature of 5 C”. If the system is thermally insulated from the surroundings, what is the mass of the copper bowl? The specific heat capacities of water and copper are 4180 J kg K and 386 J kg’K’, respectively. The latent heats of fusion and vaporization of water are 333 kJ kg and 2256 kJ kg’, respectively.

A). 15,6 kg
B). 10.2 kg
C). 17.8 kg
D). 14.7 kg

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Sapo 6 months 2021-07-15T09:28:01+00:00 1 Answers 3 views 0

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    0
    2021-07-15T09:29:23+00:00

    Answer:

    D.14.7 kg

    Explanation:

    Mass of block of ice=m_i=400 g=400\times 10^{-3} kg

    1 kg=1000 g

    T_1=0^{\circ}C

    T_2=30^{\circ}C

    T_3=5^{\circ}C

    Specific heat capacities of water=C_w=4180J/kgK

    Specific heat capacities of copper=C=386 J/kgk

    Latent heat of fusion=L_f=333KJ kg=333\times 10^3 Jkg

    1KJ=1000 J

    Latent heat of vaporization=L_v=2256KJkg=2256\times 10^3Jkg

    m_Cu C(T_2-T_3)=m_iL_f+m_iC_w(T_3-T_1)

    Substitute the values

    m_Cu\times 386(30-5)=400\times 10^{-3}\times 333\times 10^3+400\times 10^{-3}\times 4180(5-0)

    m_{Cu}(25)(386)=141560

    m_{Cu}=\frac{141560}{25\times 386}=14.7 kg

    Hence, the mass of copper bowl=14.7 kg

    Option D is true.

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