ANALYSIS
Derived from the Latin word “calor” (meaning heat), and the Greek term “metry” (to measure), Calorimetry is the science of measuring the amount of heat. This means that all calorimetric techniques are therefore based on the measurement measurement of heat that may be generated (in an exothermic exothermic process), consumed (endothermic), or simply dissipated by a sample. Experiment 302 focuses on the former two – heat lost and heat gained.
It should also be noted that calorimetry makes use of the law of heat exchange, which states that in an isolated system, the amount of heat given up by the hotter body is equal to the amount of heat absorbed by the colder body. In this case, the isolated system is the calorimeter and its contents. This relationship relationship (referring to the numerical value of heat) thus gives the equation: Qloss = Qgained
Equation 1
But since their signs will be opposite (lost = (-) & gained = (+)), this equation can be rewritten as: as: Qloss + Qgained = 0
Equation 1.1
Another equation to take note of is the equation for heat, involving the specific heat of a body (c), as shown below.
Equation 2
Where: Q = heat (cal) m = mass (g) ∆T = change in temperature, Final Temperature Temperature – – Initial Initial Temperature (C )
Materials Used for the Duration of the Experiment
The first part of the experiment utilized these first two equations, established the relationship between them and derived an equation in order to solve for the experimental value of the specific heats of both aluminum and copper. The resulting equation is as follows:
From the equation above, the values of certain data required can be inferred. Among these include: Water: mass, specific heat, change in temperature Calorimeter: mass, specific heat, change in temperature Metal: mass, change in temperature
After measuring these values, the specific heats of the two sample metals were calculated separately (in two trials). Refer to the table of data for Part 1. These values were then compared to the actual/accepted values listed in the table of specific heats. The results yielded moderately high percentages of error – 19.78% and 25.21% respectively. These were most likely caused by erroneous readings from the electronic scale, and the thermometer. Part 1. Determining the Specific Heat of Metals Trial 1. Aluminum 45.6 g Mass of metal, mm 46.4 g Mass of calorimeter, mc 233.33 g Mass of water, mw Initial Temperature of metal, t om 71 C Initial Temperature of Calorimeter, t oc 28 C Initial Temperature of Water, t ow 28 C Final Temperature of Mixture, t mix 30 C Experimental Specific Heat of Metal, c m 0.2604 cal/g-C Actual Specific Heat of Metal, c m 0.2174 cal/g-C 19.78% Percentage of Error
Substance Aluminum Beryllium Brass Copper Ethanol Ice Iron Lead Mercury
c, specific heat capacity
Trial 2. Copper 19.9 g 46.4 g 150 g 72 C 29 C 29 C 30 C 0.1167 cal/g-C 0.0932 cal/g-C 25.21%
0.2174 0.4760 0.0917 0.0932 0.5800 0.5017 0.1123 0.0310 0.0329 Part 1 of the Experiment. (Dipping the metal sample in boiling water)
Salt Silver Water
0.2100 0.0560 1.000
The second part of this experiment dealt with the experimental determination of the latent heat of fusion of ice (L f ). The latent heat of a substance refers to the amount of heat needed to change the phase of unit mass without any change in temperature. The latent heat of fusion is used for situations that involve change of phase from solid to liquid, or vice versa. On the other hand, the latent heat of vaporization (Lv) is used for phase changes from liquid to gas or vice versa. The equations for heat involving latent heat are as follows:
Equation 3
.......
Note: The signs (+/-) depend on what kind of process is taking place (endothermic/exothermic) Using equations 1-3, an equation wherein Lf is isolated can be derived, and the resulting equation is shown below.
Again, the values needed to completely solve for Lf can be inferred, and these are: Water: mass, specific heat, change in temperature Calorimeter: mass, specific heat, change in temperature Ice: mass, change in temperature
After getting these values, experimentally, the latent heat of fusion of ice was computed (in two trials). Again, these were compared to the actual specific latent heat of fusion of ice, which is 80 cal/g.
The percentage errors yielded were 13.78% and 2.31% for trials 1 and 2, respectively.
Part 2. Latent Heat of Fusion of Ice Mass of calorimeter, mc Mass of water, mw Mass of mixture, mmix Mass of ice, mi Initial Temperature of Ice, toi Initial Temperature of Calorimeter, t oc Initial Temperature of Water, t ow Final Temperature of Mixture, t mix Experimental Latent Heat of Fusion, L f Actual Specific Latent Heat of Fusion, Lf Percentage of Error
Trial 1 46.4 g 229.8 g 257.3 g 27.5g 0 C 28 C 28 C 19 C 69.98 cal/g 80 cal/g
Trial 2 46.4 g 196.4 g 215.4 g 18.8g 0 C 20 C 20 C 12 C 81.85 cal/g 80 cal/g
13.78%
2.31%
It should be noted that multiple erroneous or inaccurate readings from the thermometer can be disastrous to the experiment, as temperatures of the samples, the calorimeter, and the equilibrium temperature play a large part in all of the equations used for this experiment. This was what most likely cau sed the unusually high percentage errors of the results yielded.
CONCLUSION
As an experiment highlighting the use of calorimetry and the concept of heat, E302 focused on using an isolated system (a calorimeter) in order to solve for the experimental values of two properties of the samples given. In particular, performance of experiment 302 involved the calculation of the specific heat of two sample metals, particularly aluminum and copper, and the determination of the latent heat of fusion of ice. The first part dealt with the specific heat of the two metals. After gathering the relevant data, the following equation was then used to determine cm:
This value would then be treated as the experimental value of c and then compared to the accepted value listed on the table of specific heats. The second part of the experiment was all about computing for the experimental specific latent heat of fusion of ice, wherein two trials were performed. Again, the required data were first measured/gathered, and then the following equation, derived from the law of heat exchange, was used:
Like the first part, this value would be compared to the actual value and the percentage of error was calculated.
