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

1 Answer
Apr 25, 2017

Answer:

#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#