If 7.00 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the f

Question

If 7.00 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the final temp.
How much ice remains, if any?
I don't need the final temp, but how much ice remains in Kg. Thanks If 7.00 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the final temp.
How much ice remains, if any?
I don't need the final temp, but how much ice remains in Kg. Thanks If 7.00 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the final temp.
How much ice remains, if any?
I don't need the final temp, but how much ice remains in Kg. Thanks

Explanation / Answer

we know, specifica heat of ice, c_ice = 2030 J/(kg K)

Latent heat of fusion of ice, Lf = 3.33*10^5 J/kg

specific heat of ice, C = 4186 J/(kg K)

Amount of heat gained by ice when it comes from -5 to 0C,

Q1 = m_ice*C_ice*(0 - (-5))

Q1 = 7*2030*5 = 71050 J

Amount energy gained when ice melt, Q2 = m_ice*Lf

Q2 = 7*3.33*10^5 = 2338000 J

Amount of heat lost by water when it comes from 30 to 0,

Q3 = m_water*C_water*(30 - 0)

Q3 = 12*4186*(30 - 0)

Q3 = 1506960 J

clearly, Q1 + Q2 > Q3

so, total ice do not melt.

let m is the mass of ice that melts,

m*Lf = (Q3 - Q1)

m = (Q3 - Q1)/Lf

m = (1506960 - 71050)/(3.33*10^5)

m = 4.312 kg

final temperature = 0 C

mass of remaining ice = 7 - 4.26 = 2.688 kgs ice remains

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