Phase changes and energy conservation

AI Thread Summary
To find the equilibrium temperature of the system involving a 35-g ice cube, 110 g of water, and a 62 g aluminum cup, the energy gained by the ice melting must equal the energy lost by the water and the cup. The correct approach involves using the equations for heat transfer, considering both the phase change of the ice and the temperature changes of the water and cup. When replacing the aluminum cup with a silver cup of equal mass, the equilibrium temperature will be higher due to silver's lower specific heat capacity compared to aluminum, resulting in less energy required to raise the temperature. The discussion emphasizes the importance of accounting for both phase changes and temperature changes in thermal equilibrium calculations. Understanding these concepts is crucial for solving similar problems in thermodynamics.
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Homework Statement


A 35-g ice cube at 0.0 C is added to 110 g of water in a 62 g aluminum cup. The cup and the water have an initial temperature of 23 C.

a. Fine the equilibrium temperature of the cup and its contents

b. Suppose the aluminum cup is replaced with one of equal mass made from silver. Is the equilibrium temperature with the silver cup greater than, less than, or the same as with the aluminum cup? Explain.

Homework Equations


Q = mL
Q = mc(change in T)
cwater = 4186
cice = 2090
caluminum=900
Lice = 33.5 x 10^4

The Attempt at a Solution


]3. The Attempt at a Solution [/b]
I set the mL = [mwcw(Tfw-Tiw) + maca(Tfa - Tia)]
but that seems wrong, and there are another 20 steps after, so I'm going to not put that here
 
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When you made the energy gained equal the energy lost, you only took into account the phase change from ice to water (Q = mL). After it has made the change, it is now water at 0 degrees, right?
 

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