Thermal equilibrium with water and ice

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SUMMARY

The discussion centers on calculating the mass of ice in a thermal equilibrium scenario involving a 3.8 kg copper block at 72°C and a mixture of ice and water totaling 1.2 kg, reaching an equilibrium temperature of 8°C. The heat transfer equation used is Mice(Lf) + (Mwater)(Cwater)(Teq - Ti) = (Mcopper)(Ccopper)(Ti - Teq). The challenge arises from the unknown initial temperature (Ti) of the water, which is critical for solving the equation. The key insight is recognizing that the mixture of ice and water is at the same temperature, which is 0°C.

PREREQUISITES
  • Understanding of thermal equilibrium concepts
  • Knowledge of heat transfer equations
  • Familiarity with specific heat capacities (Cwater, Ccopper)
  • Basic principles of phase changes (latent heat of fusion)
NEXT STEPS
  • Study the principles of thermal equilibrium in detail
  • Learn about latent heat calculations, specifically latent heat of fusion (Lf)
  • Explore specific heat capacity values for various materials
  • Practice solving heat transfer problems involving phase changes
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Students in physics or engineering, educators teaching thermodynamics, and anyone interested in heat transfer calculations involving phase changes.

louisfrancois
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A 3.8 kg block of copper at a temperature of 72C is dropped into a bucket containing a mixture of ice and water whose total mass is 1.2 kg. when thermal equilibrium is reached, the temperature of the water is 8C. How much ice was in the bucket before the copper block was placed in it? (Neglect heat capacity of the bucket).

Heat gained=heat lost
Mice(Lf)+(Mwater)(Cwater)(Teq-Ti)=(Mcopper)(Ccopper)(Ti-Teq)

then i tried to solve for the mass of the ice, but the Ti of water is also unknown so I could not solve it. Also, it said to ignore the heat capacity of the bucket,so i left it out of the equation completely.

Thanks for any help!
 
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the Ti of water is also unknown
Think about the statement "a mixture of ice and water". Assuming the ice and water are in thermal equilibrium - what is the temperature? We have two phases solid and liquid at the same temperature, which is . . . ?
 

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