# Specific heat lab question

1. Sep 24, 2008

### emperrotta

For my most recent lab, the goal was to find the specific heat of lead metal shot. The procedure of the experiment consisted of using the method of mixtures. In this procedure, the room temperature Tr is first measured. Then, an insulated calorimeter cup is filled with water, and the temperature of the water Tw is measured. Meanwhile, lead metal shot is placed in a cup, which in turn is placed in boiling water until the temperature of the metal shot Tm reaches about 100 degrees Celsius depending on the calibration of the thermometer. Once the temperature of the metal shot reaches its high point near 100 degrees Celsius, the temperature is recorded and the metal shot is poured into the water. The metal shot then releases heat which is absorbed by the water until the mixture reaches thermal equilibrium and this final temperature Tf is measured.

The formula for specific heat is:
Q = c m dT
Q = heat released or absorbed
c = specific heat
m = mass
dT = change in temperature

With this procedure, once the metal is poured into the calorimeter the following occurs:
heat lost = heat gained
Qmetal shot = Qwater + Qcalorimeter

The final equation that was used to determine the specific heat of the metal shot was:
mmcm(Tm-Tf) = (mwcw + mccc)(TfTw)
mm = mass of metal shot
cm = specific heat of metal shot
Tm = temperature of heated metal shot
Tf = final temperature after metal shot was poured into the calorimeter with water
mw = mass of water
cw = specific heat of water
mc = mass of calorimeter cup
cc = specific heat of calorimeter cup
Tw = temperature of water before the metal shot is poured into it

It is stated in the lab procedure that the final temperature Tf should be above room temperature Tr by about as many degrees as Tw was below it such that Tf - Tr = Tr - Tw. If this is approximately the case, the best results will be achieved.

After all this, can someone tell me why satisfying the above scenario will provide the best results? Thanks in advance.