Why Does Equilibrium Temperature in a Specific Heat Lab Ensure Accurate Results?

[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.

 

[anathema]

Thank you for sharing your lab procedure and equations for finding the specific heat of lead metal shot. The scenario you described, where the final temperature Tf is above room temperature Tr by about the same amount that Tw was below it, is ideal for achieving the most accurate results. This is because it ensures that the heat lost by the metal shot is equal to the heat gained by the water and calorimeter. In other words, the system has reached thermal equilibrium, meaning that there is no more transfer of heat between the metal shot and the water/calorimeter. This allows for a more accurate measurement of the specific heat of the metal shot, as any additional heat transfer after this point would affect the final temperature and thus the calculated specific heat.

In addition, this scenario also minimizes any heat loss to the surroundings, as the final temperature is closer to the initial room temperature. This helps to reduce any errors in the measurement and calculation of the specific heat.

I hope this helps to explain why satisfying this scenario will provide the best results. If you have any further questions, please let me know. Best of luck with your experiment!

 

[baba89]

I can explain why satisfying the above scenario will provide the best results for determining the specific heat of the metal shot. In this experiment, the goal is to accurately measure the amount of heat released by the metal shot and the amount of heat absorbed by the water and calorimeter. This information can then be used to calculate the specific heat of the metal shot using the formula Q = c m dT.

The key to obtaining accurate results is ensuring that the system reaches thermal equilibrium, meaning that the heat lost by the metal shot is equal to the heat gained by the water and calorimeter. This is represented by the equation Qmetal shot = Qwater + Qcalorimeter.

In order for this equation to hold true, the final temperature Tf must be above the initial room temperature Tr by the same amount that the water temperature Tw was below it. This ensures that the heat lost by the metal shot is equal to the heat gained by the water and calorimeter, resulting in a balanced equation.

If the final temperature Tf is not above the room temperature Tr by the same amount as Tw was below it, the equation will not be balanced and the results will be inaccurate. This is because the system has not reached thermal equilibrium and there is still heat being exchanged between the metal shot and the water/calorimeter.

Therefore, satisfying the above scenario will provide the best results because it ensures that the system is in thermal equilibrium and the equation Qmetal shot = Qwater + Qcalorimeter holds true, leading to accurate calculations of the specific heat of the metal shot.