8. (21 pts total) You are making a bowl of 500 g of broth for a sick kid, and ne

Question

8. (21 pts total) You are making a bowl of 500 g of broth for a sick kid, and need to cool it down for them to a final temperature of 65 °C. You place a 35 g ice cube initially at-17-C into the bowl and wait for it to melt and reach equilibrium. Assume the bowl absorbs no heat. Take the specific heat of broth and to be 4186 J/kg-K, the latent heat of fusion of water to be 3.34 x 10* J/kg the specific heat of ice to 2090 J/kg K, and remember that the melting point of ice is o °C water and former ice) in reaching the equilibrium a. Determine the total energy absorbed by the 35 g of ice ( temperature b. Determine the initial temperature of the broth.

Explanation / Answer

mass of the bowl, mb=500g

final temperature, Tf=65 oC

mass of the ice, m_ice=35 g

initial temperature,Ti=17 oC

a)

heat absorbed, Q=m_ice*C_ice*dT + m_ice*L_fusion + m_ice*C_water*dT

=m_ice*(C_ice*dT + L_fusion + C_water*dT)

=35*10^-3*(2090*(17) + 3.34*10^5 + 4186*(65))

=22456.7 J

b)

Q=m_bowl*C_bowl*dT

22456.7=500*10^-3*4186*(Ti-65)

===> Ti=75.73 oC

initial temperature of bowl is Ti=75.73 oC

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