What Is the Equilibrium Temperature When Aluminum Meets Water?

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SUMMARY

The equilibrium temperature when a 150g aluminum cylinder at -196°C is placed in 60g of water at 15°C can be calculated using the principle of conservation of energy. The relevant equations include Q(water) = m(water) c(water) (∆T) and Q(aluminum) = m(aluminum) c(aluminum)(∆T). The heat lost by the water equals the heat gained by the aluminum, leading to the equation: HeatLost = HeatGained. This approach allows for the determination of the final equilibrium temperature of the system.

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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 °celsius. In which case...

HeatLost = HeatGained

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

HeatGained = MassAluminium*SpecificHeatAluminium*(FinalTemp-InitialAluminiumTemp)
 

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