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

Question

Wyatt Atkins · Accepted Answer

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

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#

Luna Chen · Answer

undefined To find the specific heat of an unknown metal, you can use the method of mixtures. First, heat a known mass of the metal to a known temperature. Then, transfer the metal to a calorimeter containing a known mass of water at a known initial temperature. Measure the final equilibrium temperature of the system. Finally, use the heat gained by the water (q_water = m_water * c_water * ΔT) equal to the heat lost by the metal (q_metal = m_metal * c_metal * ΔT) to solve for the specific heat of the metal (c_metal).