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

Apr 25, 2017

$0.165 \left(\frac{J}{k g \cdot K}\right)$
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 $4.178 \left(\frac{J}{g {\cdot}^{o} K}\right) .$ Heat available from the object: 14.93g * ?(J/(g*^oK))* delta T^oK_m = $71.5 g \cdot 4.178 \left(\frac{J}{g {\cdot}^{o} K}\right) \cdot \delta {T}^{o} {K}_{w}$ required to heat the water.

$\delta {T}^{o} m$ = 99 – 26.2 = 72.8 (the 99’C mentioned is the water bath temperature used to heat the metal for this experiment).

$\delta {T}^{o} w$ = 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 = $71.5 g \cdot 4.178 \left(\frac{J}{g {\cdot}^{o} K}\right) \cdot 0.6$
1086.9 * ?(J/(g*^oK))  = $179.2$
?(J/(g*^oK)) = 0.165