How Do You Calculate the Mass of an Aluminum Cup in a Heat Transfer Problem?

[Knfoster]

Homework Statement

An aluminum cup contains 217g of water at 21.2oC. A 404g sample of silver at an initial temperature of 80.8oC is placed in the water. A 41.0g copper stirrer is used to stir the mixture until it reaches its final equilibrium temperature of 25.7oC. Calculate the mass of the aluminum cup.

Homework Equations

Q=mCdeltaT
heat lost=heat gained

The Attempt at a Solution

Could someone please help me set the problem up w/o numbers. Thanks.

 

[Redbelly98]

You have the right equations to work with, maybe listing a few facts will help get you going:

Every object will end up at the final temperature of 25.7C.

Each object either loses heat, or gains heat. That tells you on which side of the heat lost=heat gained equation each object belongs.

Presumably the copper stirrer also starts out at 21.2C.

 

[nlightner]

I would approach this problem by first identifying the known quantities and variables. In this case, we are given the mass of water (217g), the initial temperature of the silver (80.8oC), the final equilibrium temperature (25.7oC), and the mass of the copper stirrer (41.0g). The unknown variable is the mass of the aluminum cup.

Next, I would use the heat equation Q=mCdeltaT to calculate the heat lost by the silver and the heat gained by the water. Since the system is in equilibrium, these two values should be equal. This will allow us to set up an equation and solve for the unknown mass of aluminum.

Finally, I would plug in the given numbers and solve for the mass of the aluminum cup. This will give us the final answer and complete the problem. It is important to remember to use the correct units and to pay attention to the signs of the values (i.e. negative for heat lost and positive for heat gained).