Introduction
One gram of water takes 4.184 joules of energy to increase its temperature 1 ºC. This is the most energy any substance takes to raise its temperature 1 ºC. In contrast to taking the most energy to raise its temperature 1 ºC, this means that it also takes the longest to cool down. This means that water has the highest heat capacity. It must release 4.184 joules of energy in order to decrease its temperature by just 1 ºC. The heat water releases is absorbed by its environment. Knowing the heat capacity of water, it is possible to find how well its environment insulates it. Also using the heat capacity of water, one can figure out the heat capacity of an unknown substance by putting it in water and measure the temperature change of the water and the unknown substance. In this experiment, this is exactly what was performed.
Experimental
First, an empty Styrofoam cup and lid were weighed and its mass was recorded. 70 mL of room temperature water was then added to the Styrofoam cup and it was reweighed and recorded. The temperature of the water was also recorded. Next, 30 mL of water was heated until boiling and this temperature was also recorded. The boiling water was poured into the Styrofoam cup and the final temperature of the combined water was measured and recorded. The final mass of the cup was also recorded.
For the next part of the experiment, an empty Styrofoam cup and lid were again weighed and its mass was recorded. 100 mL of room temperature water was added to the cup and it was reweighed and recorded. The temperature of the water was also recorded. Next, an unknown metal was heated to about 100 ºC and then poured into the Styrofoam cup. The final temperature of the water was measured and recorded, as was the final mass of the cup.
Results
Identification of Metal: 12
Determination of Calorimeter Constant, B:
| Trial 1 | Trial 2 | |
| Mass of empty Styrofoam cup | 3.56 g | 3.55 g |
| Mass of cup + 70 mL water | 72.20 g | 73.26 g |
| Mass of cup + 70 mL water + 30 mL hot water | 101.57 g | 102.88 g |
| Initial temperature of water in calorimeter | 23.70 ºC | 24.20 ºC |
| Temperature of the boiling water bath | 99.5 ºC | 99.5 ºC |
| Final temperature of calorimeter + added hot water | 43.99 ºC | 44.3 ºC |
| Mass of cool water in cup, mCW | 68.64 g | 69.71 g |
| Mass of added hot water, mHW | 29.37 g | 29.62 g |
| Temperature change of cool water in calorimeter, ΔTCW | 20.29 ºC, 293.29 K | 20.1 ºC, 293.1 K |
| Temperature change of added hot water, ΔTHW | 55.5 ºC, 328.5 K | 55.2 ºC, 328.2 K |
| Calorimeter constant, B | -425. J/K | -430. J/K |
Determination of the Heat Capacity of a Metal:
| Trial 1 | Trial 2 | |
| Mass of empty Styrofoam cup | 3.59 g | 3.58 g |
| Mass of cup + 100 mL water | 103.40 g | 103.33 g |
| Mass of cup + 100 mL water + hot metal | 180.97 g | 180.90 g |
| Initial temperature of water in calorimeter | 24.35 ºC | 23.9 ºC |
| Temperature of boiling water bath | 99.0 ºC | 99.5 ºC |
| Final temperature of calorimeter + added hot metal | 29.75 ºC | 29.375 ºC |
| Mass of cool water in cup, mCW | 99.81 g | 99.75 g |
| Mass of added hot metal, mHM | 77.57 g | 77.57 g |
| Temperature change of cool water in the calorimeter, ΔTCW | 5.40 ºC, 278.40 K | 5.5 ºC, 278.5 K |
| Temperature change of added hot metal, ΔTHM | 69.3 ºC, 342.3 K | 70.1 ºC, 343.1 K |
| Heat capacity of metal, CP, M | 0.0775 J/gK | 0.132 J/gK |
| Molar mass of metal | 323. g/mole | 189. g/mole |
Calculations
For the determination of the calorimeter constant, to find the mass of cool water in the cup, I simply subtracted the mass of the empty cup from the mass of the cup with 70 mL of water. To find the mass of hot water added, I subtracted the mass the cup with 70 mL of water from the mass of the cup with the 70 mL of cool water and 30 mL of hot water. To find the temperature changes, I found the difference in temperatures between the final and the initial readings. I then converted those temperatures to Kelvin from Celsius by adding 273. To find the calorimeter constant, I used the equation B = -CP(mCW ΔTCW + mHW ΔTHW) / ΔTCW.
For the determination of the heat capacity of a metal, I performed the same operation as I did for the determination of the calorimeter constant, only replacing the mass of hot water with the mass of the hot metal. The equation for the heat capacity of the metal was also different. It was CP, M = – ΔTCW (B + mCW CP) / (mHM ΔTHM). Lastly, to find the molar mass of the metal, I then divided 25 J/mole K by the heat capacity of the metal, which is the Law of Dulong and Petit.
Discussion/Conclusions
My final results do not seem very accurate. The calorimeter constants seem fairly close, but that difference affected the result of the heat capacity of my metal greatly. If I had gotten the same calorimeter constant for both trials, then the heat capacity of the metals would have came out nearly equal. As a result of the heat capacity of the metals being different, their molar masses were also thrown off. In conclusion, I must have made a mistake in a reading while finding the calorimeter constant.
Something that surprised me was how low the heat capacity of the metal was. Normally I think of metals as being very hot and staying hot, but this experiment proved how metals actually cool very quickly. People usually make this generalization, but they are wrong. I think it is because metals heat up more quickly, so they typically think they stay hot. In actuality, hot water is more dangerous than hot metal.
