# Calorimetry Problem, calculating the specific heat of a unknown substance

#### klawlor419

1. Homework Statement
A 500.0-g chunk of unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at room temperature (20.0 C). After waiting and stirring for 5.00 minutes, you observe that the water's temperature has reached a constant value of 22.0 C.

(a) Assuming that the styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat of the metal?

parts (b) and (c) are separate easier questions, not relevant to (a).

2. Homework Equations
Q=m c ΔT
Q(metal)=-Q(water)

Temp boiling water, 100 C, specific heat of water, 4190 J/kg-C

3. The Attempt at a Solution

First I solved to find the heat absorbed by the water from the metal, in order to raise the temperature of the water 2 C. Secondly, with the assumptions made in the problem, I assume that the heat gained by the water is exactly that lost by the metal. Equating these terms and getting an equation for the specific heat has a problem, which is that I don't know ΔT for the metal. Im sure Im missing something simple, but I can't get around this term ΔT for the metal.

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#### gneill

Mentor
Assuming that the system has reached equilibrium (after all, the water temperature is said to have reached a constant temperature...), what temperature must the metal have?

#### klawlor419

Ah, thanks. That was simple

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