We all wish for the ideals. – Ripped, Jonaxx
Here’s the last report for the last experiment of Physics 103.1 for this semester. Our group’s data were quite disastrous to interpret but since this is our assigned topic for the last oral presentation, I have to make this better than my other blog reports.
Heat is energy in transit. Calorimetry is used to determine the heat released or absorbed in a chemical reaction. Calorimeters are devices used to measure the changes of the thermodynamic quantities in a reaction. There are two main types of calorimeters; a coffee cup calorimeter, which determines the heat of a solution reaction at constant atmospheric pressure, and a bomb calorimeter, which measures the heat of a solution reaction at constant volume.  For the experiment, we used a coffee cup calorimeter.
The main equation for calorimetry is given by
Q = mcΔT (1)
where the amount of heat Q is given by the product of the mass m, specific heat capacity c, which is an intrinsic property of the object, and the change in temperature ΔT, the difference between the final and initial temperatures. The specific heat capacity of water is 4.184 4.184 J/g-°C.
Heat lost is negative in convention since temperature goes from high to low while heat gained is positive in convention since lower temperature goes higher.
The objectives of the experiment are
- to determine the heat capacity C of the coffee cup calorimeter calorimeter
- to determine the specific heat capacities c of the metal samples
- to compare the theoretical and experimental values of the specific heat capacities of the metal samples
Heat Capacity of the Coffee Cup Calorimeter
The first part of the experiment aimed to find the heat capacity C of the coffee cup calorimeter.
The heat capacity of a defined system is the amount of heat (usually expressed in calories, kilocalories, or joules) needed to raise the system’s temperature by one degree (usually expressed in Celsius or Kelvin). 
The amount of heat gained by the calorimeter is given by the product of the heat capacity C of the calorimeter and the change in temperature ΔT.
qgained by sample = CcalorimeterΔT (2)
qlost by hot water = qgained by calorimeter + qgained by tap water (3)
To find the heat capacity of the calorimeter, equations (1), (2), and (3) are used.
Ccalorimeter = [mhotchot (Thot – Tfinal) – mtapctap (Tfinal – Ttap)] / (Tfinal – Ttap) (4)
For the first part of the experiment, a coffee cup calorimeter, connected to a thermocouple probe (digital thermometer) dipped inside without touching the bottom, was filled with 50 mL tap water, temperature measured as 27.2 °C. Another 50 mL of water, boiled to 93.4 °C, was put to the calorimeter. The temperature was monitored and measured at 30-second time interval for 5 minutes. This will serve as the calibration of the calorimeter, to determine its capacity and the amount of heat it can absorb from the sample.
Figure 1. Coffee cup calorimeter setup
The data gathered were put into a logarithm of temperature vs. time plot.
Figure 2. Plot of the logarithm of temperature as a function of time
From the exponential y-intercept of the calibration curve, the mixing temperature of the system was obtained as 39.2 °C. This will serve as the final temperature of the system.
The volumes of the tap water and hot water are equal. These were converted to masses using the density of the water which is 1.00 g/mL. The heat capacity of the calorimeter Ccalorimeter was calculated using (4) as 739.55 T/°C. This is a relatively high heat capacity but since the coffee cup calorimeter is made of polystyrene, which is a good insulator, this value is reasonable enough.
Specific Heat Capacities of Copper and Aluminum
The second part of the experiment used the same coffee cup calorimeter to determine the specific heat capacities of copper and aluminum.
Specific heat capacity c is the amount of heat needed to raise one degree Celsius of a unit mass. This is an intrinsic property of an object that is dependent on the material composition of the object.
qlost by sample= qgained by calorimeter + qgained by tap water (5)
To determine the specific heat of the metal sample, equations (1), (2) and (3) are used.
csample = [mtapctap (Tfinal – Ttap) + Ccalorimeter(Tfinal – Ttap)] / msample(Tsample – Tfinal) (6)
Note that all heat gained has the initial temperature of the tap water subtracted from the final temperature of the system while the heat lost subtracted the final temperature from the mass of the sample. This is because heat lost should come from a higher temperature then to a lower temperature.
For the setup of the second part of the experiment, the same coffee cup calorimeter was used with the thermocouple probe dipped into 50 mL tap water but, not touching the bottom of the calorimeter. The temperature of the tap water was measured. The metal samples, weighed using a weighing scale, were boiled then, put inside the calorimeter. The temperature of the boiled samples were also measured. The temperature inside the calorimeter was monitored and recorded at 30-second time intervals in 5 minutes.
Figure 3. Setup for determining the specific heat capacities of copper (dark brown) and aluminum (gray)
The temperature data gathered were put into a logarithm of temperature vs. time plot for each metal sample.
Figure 4. Logarithm of temperature as a function of time for copper Cu sample
Figure 5. Logarithm of temperature as a function of time for aluminum Al sample
The data points were expected to be linear in a logarithmic scale. In the copper sample, the temperature was fluctuating in the first 3 minutes then stabilized. In the aluminum sample, the data points still look a logarithmic plot. The R2 values also show that errors may have propagated during this part of the experiment.
Like the plot of the calibration curve, the exponential of the y-intercepts of these plots will serve as the final temperatures of each system.
Table 2 lists the data for both copper and aluminum metal samples. Following the procedure on the laboratory manual for the experiment, the final temperature of the system listed here came from the exponential of the y-intercept. The specific heat capacities were calculated using (6) as -0.116 J/g-°C for copper which yielded 130.12% error from the theoretical specific heat capacity of copper 0.385 J/g-°C and 1.998 J/g-°C for aluminum which deviated 122.00% with respect to its theoretical value 0.900 J/g-°C.  These large values of percent deviation make less precision and less accuracy. These may have been caused by errors that propagated during the experiment.
Beforehand, my groupmates and I consulted our instructor regarding our data. The temperature inside the calorimeter should ideally increase upon putting the hot metal samples however, the temperature fluctuated on the first three minutes for copper and stabilized in the last minute for aluminum. The fluctuations in the plot for copper are due to the localized temperature of the tap water since the heat distribution will not be even at the instance that the metal sample was put into the calorimeter. The stabilization of temperature for aluminum is quite weird because it somehow shows that the system is in equilibrium at that point. Another point for copper is that, the water used is the calibrated one, the mixture of hot water and tap water, making the temperature of tap water higher thus, also making the change in temperature negative. The water used for aluminum is tap that’s why its temperature is relatively ambient.
To minimize the error, our instructor advised us to use the temperature at the fifth minute instead of following the procedure on the manual.
Table 2.1 lists the experimental heat capacities of copper and aluminum under the final temperature of the system as the temperature recorded on the fifth minute. Compared to table 2, the experimental heat capacity of copper was lower, so was the percent deviation with respect to the theoretical value. However, the experimental heat capacity for aluminum was higher than that of listed in table 2. I guess the error was minimized for copper only using this method. Theoretically and ideally, copper should have a lower specific heat capacity than aluminum since copper is a better conductor. Moreover, both methods in determining the specific heat capacities of the metals showed the same trend.
No matter how hard we try to compromise things, we still have to accept the potent truth behind the harsh reality.
Possible sources of errors are:
- the delayed closing of the calorimeter upon mixing the hot water with the tap water, also upon putting the hot metal sample inside the tap water. This could lead to heat lost in air thus, lowering the heat gained by calorimeter and by tap water so, the calorimeter must be closed immediately;
- the uncoordinated measurement, reaction time, and start of recording of the temperature upon instant mixing of the hot water and tap water, also upon putting the hot metal samples inside the calorimeter. The recording of data should start immediately upon mixing.
- the calorimeter must be properly insulated after hot water or hot metal sample is put inside to ensure that heat will not be lost to surroundings outside the calorimeter.
- the ‘tap’ water used for copper is not really tap because it was from the calibration, meaning it is a mixture of hot water and tap water making the temperature of the tap water high.
- the position of the thermocouple probe inside the calorimeter is not definite. It is dipped but since the calorimeter is closed, the exact placement inside was not visible outside and it might have touched the walls or the bottom of the calorimeter. This will affect the temperature measurements.
- the temperature on the second part was measured from the tap water. Since the calorimeter was closed, it is hard to see the exact position of the wire inside. It should be placed near the hot metal sample but, not touching it.
- the hot metal samples were not fully submerged by the tap water. This may be the reason of the high percent deviation for aluminum since the water inside the calorimeter is just 50 mL.
- the temperature was localized after putting the hot metal samples making the heat distribution uneven. This is the cause of the fluctuations in the temperature meaurements for copper.
Summary and Conclusion
To sum everything up, I still consider this experiment a success quantitatively since the objectives were met; the heat capacity of the calorimeter was determined, so do the specific heat capacities of copper and aluminum, and these were compared to the literature values. Hence, aluminum yielded a higher specific heat capacity than copper experimentally, which is also ideal even though the experimental results deviated largely from the theoretical values.
We can hope for the ideal. We can try to live like the ideal but, we can never be ideal. – Ripped, Jonaxx
 “Calorimetry.” ChemLab – Instruments – Calorimeter. Darthmouth College, n.d. Web. 23 Apr. 2016. <https://www.dartmouth.edu/~chemlab/techniques/calorimeter.html>.
 Cameron, Tracy, and Singh Ravneet. “Heat Capacity.” – Chemwiki. N.p., 02 Oct. 2013. Web. 23 Apr. 2016. <http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Thermodynamics/Calorimetry/Heat_Capacity>.
 Experiment 10: Calorimetry. Physics 103.1 Laboratory Manual. National Institute of Physics, UP Diliman, 2015-2016.
 Young, Hugh and Roger Freedman. University Physics with Modern Physics 13th edition. San Francisco: Pearson education Inc., 2012.