# How to Calculate the Specific Heat Capacity of an Unknown Metal

#### Verbally

1. Homework Statement

How can you calculate the specific heat capacity of an unknown metal? In my question the metal with a mass of 50g and a temperature of 200 degrees celsius was placed in 125 g of water with an initial temperature of 20 degrees celsius. After the simulation and the metal was placed in the water, the temperature of the water rose from 20 to 28.35. How can I find the specific heat capacity of the unknown metal? Then we have to research what metal corresponds to the resulting heat capacity.

2. Homework Equations

I know you have to use the original equation of ΔE=m*ΔT*c and rearrange it to isolate "c", thus resulting in the equation of c=ΔE/m*ΔT. But how do you calculate ΔE?

3. The Attempt at a Solution

What I did first is try to find ΔE:

= m x (T2-T1)
= 125 x (28.35-20)
= 125 x 8.35
= 1043.75 Calories = 4445.5 Joules

Then you can substitute that into c=ΔE/m*ΔT

c = 4445.5J / 125 x 8.35
= 4445.5 / 1043.75
= 4.3

I know I went wrong somewhere, could someone please explain to me where I did? I've been stuggling on this question forever!

Thanks.

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#### Borek

Mentor
Heat lost by metal equals heat gained by water.

#### Verbally

Heat lost by metal equals heat gained by water.
Ok, but how do you find the heat gained by water?

#### Fewmet

You could find the heat change in the water by reasoning from the definition that 1 calorie raises 1 g of water by 1 degree Celsius. That and the data you have let you get the answer through dimensional analysis.

If you want to be more mechanical (and, arguably, more efficient), you also have an equation that relates the change of temperature, mass, specific heat and change of heat content.

Do you see it?

#### Borek

Mentor
Ok, but how do you find the heat gained by water?
From the same m*ΔT*c - just for water.

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