Stuck on this phase change question

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SUMMARY

The discussion focuses on calculating the final temperature when ice at -10 degrees Celsius is dropped into water at 20 degrees Celsius. The key equations involved are Q = m·c·ΔT for temperature changes and Q = m·l for phase changes. The total heat required to raise the ice to 0 degrees Celsius and to melt it, denoted as H1, must be compared to the heat lost by the water, H2, as it cools to 0 degrees Celsius. Depending on the relationship between H1 and H2, the final temperature can be determined using the appropriate thermal equations.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the specific heat capacity of water and ice.
  • Knowledge of phase change concepts and latent heat.
  • Ability to manipulate and solve equations involving mass, temperature, and heat.
NEXT STEPS
  • Study the specific heat capacity values for water and ice to apply in calculations.
  • Learn about latent heat and its role in phase changes, particularly for ice melting.
  • Practice solving heat transfer problems involving multiple phases and temperature changes.
  • Explore advanced thermodynamic concepts such as equilibrium and energy conservation in closed systems.
USEFUL FOR

This discussion is beneficial for students in physics or chemistry, educators teaching thermodynamics, and anyone involved in heat transfer calculations or phase change analysis.

dan greig
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I have a question on dropping ice (-10 celsius) into water (20 celsius). What is the final temp?

i have used Q = m.c.delta T between -10 and 0

I know i have to use Q = m.l for the phase change and then agian use

Q = m.c. delta T to find a final temp.

How do i relate these two equations to each other to find the final temp?
 
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You didn't say how much ice or how much water. First calculate how much heat it would take to raise the temperature of the ice to 0 and how much heat it would take to melt the ice. Call the sum of those H1. If H1 is larger than the heat the water would lose in dropping to 0 celsius, H2, then not all the ice will melt and the final temperature will be 0 celsius.

If H2 is larger than H1, use m.c. delta T= H2-H1 to determine the temperature of the water after the ice has melted (but is still at 0 celsius). Of course the c you use for water will be different from that for ice and their masses will be different. Call that T1. Finally, use m(ice water)delta T= m(water)delta T to solve for the final temperature.
 

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