Shaho Zagrosi - University of Southampton
This experiment aimed to estimate an experimental value for the specific heat capacities of aluminium and copper, thus validating specific heat theory in turn.
Measured masses of each metal specimen were heated and subsequently added to a calorimeter containing a known mass of water. Temperature changes in the metal and calorimeter were recorded, allowing for the specific heat capacities of the metal specimens to be approximated mathematically through specific heat theory.
Experimentally derived values of specific heat capacity were $320 \space Jkg^{-1}K^{-1}$ for copper and $874 \space Jkg^{-1}K^{-1}$ for aluminium with percent error to reference values of $16.7 \%$ and $2.56 \%$ respectively. Results satisfied the aim of the experiment, both in estimating values for specific heat of metal specimens within an acceptable margin of error and in validating specific heat theory.
Further trials would benefit in reducing the impact of experimental error so that approximations are closer to reference values.
Calorimetry is an experimental procedure by which we can measure heat transfer involved chemical or physical processes. [1]
This experiment involves a physical process in which heat energy transfer is taking place from a heated metal specimen (copper or aluminium) to water contained within an insulated calorimeter. Specific heat theory, through calorimetric measurements, allows the amount of energy transfer to be quantified and to henceforth calculate the specific heat properties of the metal specimens involved.
We started with the hypothesis that experimentally derived specific heat capacity values for copper and aluminium would be within a defined margin of error of the known reference values $(<20\%)$, accounting for expected sources of error that rudimental calorimetry of this calibre would produce. We also expected the experimental value of specific heat for copper to be significantly lower than that of aluminium, owing to its properties as an efficient thermal conductor. [2]
Differences in experimental values obtained for each metal specimen's specific heat would further validate specific heat theory and the underlying laws of thermodynamics that govern specific heat. In doing so, this experiment verifies the intensive thermal properties of each metal specimen that justify their uses in engineering applications. [3]
We have been familiar with the notion of heat as a species since the dawn of humanity. Hot and cold are environmental conditions that have evolved with our primary senses, and have directly shaped the interactions we make with the environment around us. Specific heat theory and thermodynamics as a whole have far-reaching real-world applications, and thus the importance of studying thermodynamic properties cannot be understated.
Scottish physician Joseph Black is credited as the father figure of specific and latent heat, and thermodynamics as a whole. His experiments with ice and water in 1761 determined the difference between heat energy and temperature for the first time in history, and this paved the way for further developments in thermodynamics.
The first known calorimeter was built in 1789 by Antoine Lavoisier and Pierre Simon de La Place with the intention of measuring respiratory heat loss. James Prescott Joule would later mechanically define the numerical value of heat at 4.184 joules per calorie of work to raise the temperature of 1lb of water by one degree, now more commonly known as the specific heat capacity of water.
Germain Henri Hess would ultimately determine that the total energy of a chemical reaction stays constant regardless of the number of intermediate steps taken, forming the basis of closed-system energy conservation in calorimetry.
Subsequent milestones and developments over time would accumulate into what is known today as modern calorimetry. In better understanding specific heat through calorimetry, we are able to better choose the materials required for all sorts of applications. Low specific heat materials are better thermal conductors, hence their place in thermometers and cooking utensils, whereas high specific heat materials are better insulators, often utilised for fuel storage and energy conservation.
Thus calorimetry with respect to specific heat is an area of research that has allowed us to engineer solutions that penetrate every level of modern life, hence its importance cannot be understated. [1]
Specific heat capacity, commonly referred to as specific heat or enthalpy, is an intensive thermodynamic property that defines a substance's intrinsic relationship with energy and temperature. This relationship allows one to determine and compare the amount of energy input required to change the temperature of different specimens. [2]
Specific heat capacity is defined as follows:
"The specific heat capacity is defined as the quantity of heat (J) absorbed per unit mass (kg) of the material when its temperature increases 1 K (or 1 °C), and its units are J/(kg K) or J/(kg °C)." [4]
Specific heat theory (and this experiment in turn) is built upon and validated by the four fundamental laws of thermodynamics. These laws are generally defined as follows:
Zeroth Law of Thermodynamics:
"Two systems that are each in thermal equilibrium with a third system are in thermal equilibrium with each other."
Thus, heat is not transferred between objects in thermal equilibrium. In the context of this experiment, we can assume that all objects are at the same thermal energy when system temperature stabilises. [5]
First Law of Thermodynamics:
"Total energy of an isolated system is constant despite internal changes. Energy can be converted from one form to another, but the total amount of energy remains unchanged."
Hence, the total energy of a closed system remains constant. This means we can assume that energy output is equal to the energy input in this experiment, allowing us to determine a direct mathematical relationship between heat supplied from the specimen to heat absorbed by the other components in the system. [6]
Second Law of Thermodynamics:
"Heat cannot, by itself, be transported from a colder to a warmer body."
This attributes direction to heat transfer (from hot to cold), and consequently allows us to determine which components of our experiment are supplying or absorbing heat energy. [7]
Third Law of Thermodynamics:
"The entropy change for each chemical or physical transition between condensed phases, at temperatures very close to the absolute zero, is equal to zero." [8]
This experiment does not operate at temperatures that would make this law contextually relevant. However, it is noteworthy that there are unexpected behaviours of specific heat at temperatures approaching absolute zero. [9]
Specific heat capacity is generally defined by the formula $Q = mc \Delta T$; where $Q$ is the amount of energy supplied in Joules (J), $m$ is the mass of the substance in kilograms (kg), and $\Delta T$ is the change in temperature in degrees Kelvin (K) or Celsius ($\degree$C). [2]
According to the aforementioned laws of thermodynamics, it can be assumed that $Q_{Supplied} = Q_{Absorbed}$ in a closed system. Thus $Q_{Metal} = Q_{Calorimeter} + Q_{Water}$, as the heated metal is supplying energy to the water and calorimeter at a measured temperature.
This evaluates into $m_{Metal} \cdot c_{Metal} \cdot \Delta T_{Metal} = m_{Water} \cdot c_{Water} \cdot \Delta T_{Water} + m_{Calorimeter} \cdot c_{Calorimeter} \cdot \Delta T_{Calorimeter}$ which can be rearranged for $c_{Metal}$, expressed by the equation $c_{Metal} = \frac{m_{Water} \space \cdot \space c_{Water} \space \cdot \space \Delta T_{Water} \space + \space m_{Calorimeter} \space \cdot \space c_{Calorimeter} \space \cdot \space \Delta T_{Calorimeter}}{m_{Metal} \space \cdot \space \Delta T_{Metal}}$
This procedure was first undertaken with copper as the subject specimen, then repeated with respect to aluminium. The experiment was not repeated for each metal specimen and thus only one dataset was obtained for each.
The apparatus used in this experiment were as follows:
Figure 1: The general setup of apparatus for this experiment.
A calorimeter provides a closed system in which dependent variables can be measured in relation to an experiment's independent variables. In this experiment, the dependent variable is the temperature change of water (measured in degrees Celsius) and the independent variable is the substance used to heat the water (aluminium or copper). [1]
In this system, the masses of components are measured but assumed to be constant, and so do not affect the dependent variable. Furthermore, the calorimeter is placed within an insulated container to reduce heat loss to the surrounding environment from the bottom and sides.
A digital thermometer measuring in degrees Celsius ($\degree$C) was used to measure changes in temperature according to methodology. Thermometer resolution was to $0.1 \degree C$ with an uncertainty of $\pm 0.05 \degree C$.
Whilst it is seen as scientific convention to use degrees Kelvin (K), degrees Celsius is suffice in the context of this experiment as we are only observing a change in temperature, and both temperature scales are linear and so this will not impact data obtained.
The known reference value for the specific heat capacity of copper $(c_{Copper})$ is $384 \space Jkg^{-1}K^{-1}$. [2] This means that a relatively low amount of heat energy input is required to raise the temperature of copper, hence its uses as a thermal conductor.
The known reference value for the specific heat capacity of aluminium $(c_{Aluminium})$ is $897 \space Jkg^{-1}K^{-1}$. [2] A lot more heat energy input is required to raise the temperature of aluminium in comparison to copper; a difference of over double, or $513 \space Jkg^{-1}K^{-1}$ according to reference values. This makes aluminium relatively better as a thermal insulator than copper.
The known reference value for the specific heat capacity of water $(c_{Water})$ is $4196 \space Jkg^{-1}K^{-1}$. [2] Its high specific heat makes it a great thermal insulator, far more so than copper and aluminium, as far more energy is required to raise its temperature.
The experiment was undertaken in accordance with the following steps, recording measurements in data tables where relevant.
These steps were repeated with respect to aluminium.
The mass and temperature recordings populated the data tables for copper and aluminium enough so that calculations for specific heat capacity could be carried out.