How to Calculate the Specific Heat Capacity of an Unknown Metal

In summary, the conversation discusses how to calculate the specific heat capacity of an unknown metal through a simulation where the metal is placed in water and the resulting change in temperature is recorded. The equation used is ΔE=m*ΔT*c, and the heat gained by water can be found using this equation and the definition that 1 calorie raises 1 g of water by 1 degree Celsius. Dimensional analysis can also be used to find the answer.
  • #1
Verbally
3
0

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.

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?


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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  • #2
Heat lost by metal equals heat gained by water.
 
  • #3
Borek said:
Heat lost by metal equals heat gained by water.

Ok, but how do you find the heat gained by water?
 
  • #4
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?
 
  • #5
Verbally said:
Ok, but how do you find the heat gained by water?

From the same m*ΔT*c - just for water.
 

FAQ: How to Calculate the Specific Heat Capacity of an Unknown Metal

What is specific heat capacity?

Specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius.

Why do we need to calculate the specific heat capacity of an unknown metal?

Knowing the specific heat capacity of a substance can help in various scientific and industrial applications, such as designing heating and cooling systems or determining the energy efficiency of materials.

What information do I need to calculate the specific heat capacity of an unknown metal?

To calculate the specific heat capacity of an unknown metal, you will need the mass of the metal, the change in temperature, and the amount of heat energy required to cause the temperature change.

How do I calculate the specific heat capacity of an unknown metal?

The formula for calculating specific heat capacity is: specific heat capacity = (heat energy)/(mass x change in temperature). You can use this formula with the information gathered in the previous question to calculate the specific heat capacity of the unknown metal.

Are there any other factors that can affect the accuracy of the calculated specific heat capacity?

Yes, the accuracy of the calculated specific heat capacity may be affected by external factors such as heat loss to the surroundings, incomplete mixing of the metal, or the presence of impurities in the metal.

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