Question

200 g of an unknown metal powder at Thot = 72°C are dropped into a negligible heat capacity calorimeter containing 150 g of water at 16°C. The final equilibrium temperature is measured to be 36.6°C.

1. Calculate the specific heat of the metal powder c. c = J/kg-°C 2. Identify the metal from the list below.

Water

Beryllium

Aluminum

Silicon

Iron

Copper

Silver

Gold

Lead

3. Using the data table, calculate the specific heat per mole Cmolar of each pure substance listed below, along with the specific heat per mol of your unknown metal found above. Then, divide the specific heat per mole you obtain by the "gas constant", R = 8.31 J/mol-K, and enter these results in the third column. These numbers are now dimensionless. This is a way of checking what is called classical corresponding states: that regardless of the type of substance, their specific heats per mole depend only on their state: gas or solid. Of course "real matter" varies from this rule, but not extraordinarily so.

Substance	C molar (J/mol -degrees C)	C molar/R
Water
Iron
Copper
Unknown

4. Are these results close to 3? Discuss.

Answer 1

heat lost by metal powder = heat gained by water

mw*cw*dT1 = mpoder*cpowdwer*dT2

0.15*4190*(36.6-16) = 0.2*Cpowdwer*(72-36.6)

Cpowder = 1824.32 J/Kg-oC

+++++++++

Cpowder is BEryllium

++++++++++++

water     4190*0.018 = 75.42     75.42/8.314 = 9.07

Iron      470*0.0559 = 26.273     26.273/8.314 = 3.16

copper    390*0.0635 = 24.765      24.765/8.314 = 2.98

unknown   1824.32*0.00901 = 16.44   16.44/8.314 = 1.98