Quantifying Heat Exchange
We previously talked about how heat and other factors interact with gasses. Now on our last topic for this lab series, and the last topic for thermodynamics, we will placing numbers and equations on heat exchange.
The amount of heat required to change the temperature of an object depends on a lot of different factors. The following equation shows this relationship
where Q is the amount of heat needed, m is the mass of the object in question, c is the specific heat capacity (or the amount of heat needed to change one gram of an object by one degree C/K), and (delta)T is the change in temperature of the material. The specific heat of an object depends on the type of substance being treated. Water, one of the most used substances in thermodynamic experiments in the classroom, is known as having a high specific heat capacity at 4.184 J/(g * C). Materials with high specific heat capacities take a lot of energy to change temperature; thus, they are great for cooling down hot objects.
In todayâs experiment, we will determine the specific heat capacities of brass and copper using a method known as calorimetry.
A calorimeter is an insulated vessel, which prevents heat exchange between the interactions within the calorimeter and the surroundings. These calorimeters allow us to determine the heat capacities of an object by having it in thermal contact with another substance of known specific heat capacity (usually water) within its body. In this experiment, the calorimeter is a coffee-cup calorimeter that consists of stacked coffee cups. Styrofoam coffee-cups are usually used as they are good insulators that reduce the amount of heat that escapes to the surroundings.
They work on the basic thermodynamic law, where the sum of all total heat exchange between system and surrounds is zero, expressed in the equations:
In this experiment, we will identify the specific heat capacities of brass and copper samples by having hot samples interact with cold water within the calorimeter. When the hot sample enters the water, heat exchange occurs and energy is transferred into both the cold water and the calorimeter. The hot metal drops in temperature, losing heat, while both the water and calorimeter gain heat.
You may be wondering how we know the specific heat capacity of our calorimeter if its unique to all experimentation. That is true, there is no fixed formula for identifying the components of the calorimeter and directly computing for the specific heat capacity. Instead, we take the calorimeterâs heat capacity (the amount of energy needed to change the calorimeterâs temperature by 1 degree C/K) through calibration.Â
Calibration
Calibration of coffee-cup calorimeters involves having a reaction of known heat exchange occur within the calorimeter to find out how much heat is transferred to the calorimeter. In this activity, hot water was added to tap water, with the heat lost by the hot water equaling the sum of the heat gained by the tap water and the heat gained by the calorimeter.
Temperatures in this experiment were measured using a digital thermocouple with smallest reading 0.1 degree Celsius.
50 mL of tap water, its temperature recorded, was placed in the calorimeter. 50 mL of hot water was then taken from a boiling heat bath, with water temperature also measured, and made to mix with the tap water.
The temperature of the water in the calorimeter was then measured at thirty (30) second intervals until a total time of five (5) minutes had elapsed. Data was then graphed twice: first a graph of T (temperature) versus t (time) was made; then ln(T) vs t graphs were also done. A linear fit was placed on the ln(T) vs t graphs, and the y-intecept was taken. This y-intercept was used to take the temperature of the mixture at initial contact T0, by using EXP(y-intercept). Using equations (1), (2), and (3), the heat capacity of the calorimeter Ccal could be obtained.
This was done several times to get the best Ccal value for our calorimeter. The figures below present our data.
Figure 1. Trial 1 for calibration
Figure 2. Trial 2 for calibration
Figure 3. Trial 3 for calibration
Figure 4. Trial 4 for calibration
It was observed that during our experimentation, Ccal values would always be negative. We know this was not supposed to happen, as Ccal values are known to be negative and it requires an input of energy to increase temperature. We identified the main source of error to be an erratic thermocouple, which had difficulty reading temperatures above 40 degrees Celsius. This could have led directly to the negative values obtained as measurements would be important in this computation. We also considered limitations of the calorimeter in fully trapping heat and the presence of sediments in the water used making it having an increase in its specific heat capacity.
However, under the constraints of time and resources, we had to proceed. We continued the experiment under the assumption that this inconsistency would be a constant systematic error in the succeeding parts of the experiment. We decided to use the Trial 1 data for C at -109.53735 J/C as our Ccal.
Finding Specific Heat Capacity
We then attempted to find the specific heat of a 144.1 g brass sample and a 128.2 g copper sample (measurements taken using a digital scale of lowest reading 0.1 g) using calorimetry. The samples were placed in boiling water and had their temperatures rise to the temperature of the water (90 C). Individually, a sample was placed in 75 g of water, with temperature measured, in the calorimeter. The temperature of the water over time was measured similarly to what was done in calibration. Using the different equations again, the specific heats of the the samples were computed.
The following graphs were our ln(T) vs t graphs.
Figure 5. Specific heat capacity of brass
By determining T0 again, it was found that the specific heat capacity of brass was found to be -0.391 J/(g*C). Once again, a negative value was obtained. This could have been due to similar errors, as well as utilizing the negative Ccal value. Compared to a theoretical value of 0.380 J/(g*C) for brass, this came out at a 202.86% error. However, if we take the absolute value of the experimental specific heat capacity, we have only 2.86% error.
Figure 6. Specific heat capacity of copper
Similarly, it was found that the specific heat capacity of copper was -0.299 J/(g*C). We had the same problem of negative specific heat capacities and attribute it to the same errors. Compared to a theoretical value of 0.386 J/(g*C) for copper, the computed value had a 177.46% error, and an absolute specific heat capacity error of 22.54%.
Although it did not appear to be effective in our experimentation, calorimetry has been used in both physics and chemistry to explore thermodynamics and thermodynamic properties. We could improve this experiment by using better measurement devices and isolating our system more by increasing the quality of our calorimetry. There are other such calorimeters such as the bomb calorimeter that allow for different types of thermodynamic experimentation.
We are still discovering more and more things about thermodynamics and how heat interacts with all objects. As scientists, we aid in this discovery through our experimentations, both in our successes and failures. I hope these blog entries have inspired you to pursue the sciences, especially physics, to discover more about our world and how it works.
Until next time, thank you for reading.
REFERENCES
1.   Physics 103.1 Lab Manual, T5 Calorimetry, National Institute of Physics, Philippines, 2013. 2.   R.A Freedman, H.D. Young, University Physics with Modern Physics 13th Edition, Chapter 17, Pearson Education, San Francisco, 2012. 3. Specific heats taken from http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html












