Question

How do you find the specific heat of an unknown metal given the following information?

Answer 1

`0.165 (J/(kg*K))`
This would correspond to lead (Pb) with a published specific heat of 0.160.

Explanation:

This is a heat balance between a known (water) compound and the unknown.
We equate the two thermodynamic changes and solve for the unknown value of the specific heat of the compound. Water specific heat is `4.178 (J/(g*^oK)).` Heat available from the object: `14.93g * ?(J/(g*^oK))* delta T^oK_m` = `71.5g * 4.178 (J/(g*^oK))* delta T^oK_w` required to heat the water.

`delta T^om` = 99 – 26.2 = 72.8 (the 99’C mentioned is the water bath temperature used to heat the metal for this experiment).

`delta T^ow` = 26.2 – 25.6 = 0.6 Because both temperature values are differences, no specific conversion to ‘K needs to be made.
`14.93g * ?(J/(g*^oK))* 72.8` = `71.5g * 4.178 (J/(g*^oK))* 0.6`
`1086.9 * ?(J/(g*^oK))` = `179.2`
`?(J/(g*^oK)) = 0.165`