Specific heat lab question

[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 T_r is first measured. Then, an insulated calorimeter cup is filled with water, and the temperature of the water T_w 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 T_m 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 T_f 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
Q_{metal shot} = Q_water + Q_calorimeter

The final equation that was used to determine the specific heat of the metal shot was:
m_mc_m(T_m-T_f) = (m_wc_w + m_cc_c)(T_fT_w)
m_m = mass of metal shot
c_m = specific heat of metal shot
T_m = temperature of heated metal shot
T_f = final temperature after metal shot was poured into the calorimeter with water
m_w = mass of water
c_w = specific heat of water
m_c = mass of calorimeter cup
c_c = specific heat of calorimeter cup
T_w = temperature of water before the metal shot is poured into it

It is stated in the lab procedure that the final temperature T_f should be above room temperature T_r by about as many degrees as T_w was below it such that T_f - T_r = T_r - T_w. 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.

 

[Chestermiller]

This would minimize heat losses to the room (or gains from the room) since, on average, the contents of the cup would match the room temperature.