Thermal Equilibrium H2O(l) & H2O (s)

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SUMMARY

The thermal equilibrium temperature when mixing 0.5 kg of ice at -65°C with 3.0 kg of water at 20°C is 1.2°C. The solution utilizes the equation q=mcΔT, where q represents heat, m is mass, c is heat capacity, and ΔT is the change in temperature. The initial calculations indicated that the water's temperature would drop to 14.7°C when the ice reaches 0°C, but further analysis is required to find the final equilibrium temperature. The correct approach involves equating the heat lost by water to the heat gained by ice in a closed system.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the equation q=mcΔT for calculating heat exchange.
  • Knowledge of specific heat capacities for water and ice.
  • Basic algebra skills for solving equations.
NEXT STEPS
  • Study the concept of heat transfer in closed systems.
  • Learn how to apply the conservation of energy principle in thermal equilibrium problems.
  • Research the specific heat capacities of water and ice for accurate calculations.
  • Practice solving similar thermal equilibrium problems using the q=mcΔT equation.
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone interested in understanding heat transfer and thermal equilibrium calculations.

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Homework Statement


When you mix 0.5kg of ice which has an initial temperature of -65 celsius with 3.0kg of water which as an initial temperature 20 celsius, at what temperature do both substances come to thermal equilibrium?

Answer: 1.2 Celsius

Homework Equations



q=mc[Delta]T
[Delta]T=Q/C ; Q=heat, C=Heat capacity

The Attempt at a Solution




My Thoughts: I found out that when the ice reaches 0 celsius, the temperature of the water will go down to 14.7 celsius. I did this by using the equation q=mc[delta]T and solving for the final temp of water, which would be 14.7 when ice = 0. However, I don't know how to find the thermal equilibrium temp for this problem.

I've tried equating mc[delta]T of water + mc[delta]T of ice=0 because it is a closed system by solving for the delta T, but it didn't give me the answer.

Thanks for any help.
 
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