What Is the Equilibrium Temperature When Aluminum Meets Water?

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To find the equilibrium temperature when a 150g aluminum cylinder at -196°C is placed in 60g of water at 15°C, the principle of conservation of energy is applied, where heat lost by water equals heat gained by aluminum. The relevant equations involve calculating the heat transfer for both substances using their specific heats and mass. The discussion emphasizes the need to set the heat lost by the water equal to the heat gained by the aluminum to solve for the final temperature. The user expresses a preference for working in Kelvin rather than Celsius for the calculations. Ultimately, the equilibrium temperature can be determined by solving the heat exchange equations.
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Homework Statement


A 150g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to -196 degrees C. The cylinder is immediately placed in an insulated cup containing 60.0g of water at 15.0 degrees C. What is the equilibrium temperature of the system?


Homework Equations


Q(water) = m(water) c(water) (∆T)
Q(water to ice)= m(water) Lfusion of ice
Q(aluminum) = m(aluminum) c(aluminum)(∆T)

The Attempt at a Solution


My problem is how to find the equilibrium temperature using those equations?
 
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My preference would be to work in °Kelvin not °Celcius. In which case...

HeatLost = HeatGained

HeatLost = MassWater*SpecificHeatWater*(InitialWaterTemp-FinalTemp) + MassWater*LatentHeat

HeatGained = MassAluminium*SpecificHeatAluminium*(FinalTemp-InitialAluminiumTemp)
 

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