Physics Laboratory Report

Title (5 points)

Lab number and Title:

Lab E: Specific Heat

Name: [Placeholder] Group ID: 1

Date of Experiment: 10/10/20XX Date of Report Submission: 10/19/20XX

1. INTRODUCTION
1.1 OBJECTIVES
1. To measure the specific heat of a metal specimen using a calorimeter.
2. To come to a deeper understanding of the principle of conservation of
energy as it applies to thermal energy.

1.2 THEORETICAL BACKGROUND

Temperature is a measurement of the relative hotness or coldness of a body. To
raise the temperature of a body we add heat to the body. It is found that for
large ranges of temperature, if a material doesn't change state, the heat added
to a body is directly proportional to the change in the body's temperature and
to the mass of the body, that is:

(1) ∆Q=cm∆T

where ∆Q(in cal) is the heat added to the body, m(g) the mass of the body,
∆T(C) the change in temperature and the constant of proportionality c (which
only depends on the material, in cal/g°C) is called the specific heat. The
amount of heat required to raise the temperature of one gram of an arbitrary
substance by 1°C varies with the substance, that is different substance has
different specific heat. In general, the value of the specific heat of a solid
substance is predominantly a function of temperature, though small variation of
the specific heat occurs due to variation in pressure or volume.

When two bodies in an isolated system, initially at different temperatures are

placed in intimate contact with each other, in time they will come to
equilibrium at some common intermediate temperature. Because of energy
conservation, the quantity of heat lost by the hot object is equal to that
gained by the cold object provided that no heat is lost to the surroundings.

If a metal specimen of mass M and temperature T (T, 100°C in the experiment) is

placed in an insulated container (calorimeter) containing water which is at an
equilibrium temperature T,, the combination will reach a

final equilibrium temperature Ty. From this we can write,

(2) Mc(Tm-TF)=MWcW(TF-TC)+MCcC(TF-TC)

Where MW is the mass of water. Mc the mass of the calorimeter (with the
stirrer), cW the specific heat of the water co the specific heat of the
calorimeter and cC is the specific heat of the metal specimen.
2 EXPERIMENTAL PROCEDURE

Variables:cW= 1.00 cal/g°C

We started the experiment by measuring the mass of the specimen, the
calorimeter and stirrer, and water. Next, we started to boil a separate
container of water with the aluminum specimen in it. While the water was
boiling we measured the initial temperature of the water inside of the
calorimeter. Once the water was boiled, we put the aluminum specimen in the
calorimeter and placed the thermometer inside and covered it. We then waited
for the temperature to stabilize and took note of its value. We then repeated
this process for the copper specimen and calculated the specific heat of each
substance once the experiment was completed.
3 RESULTS
3.1 EXPERIMENTAL DATA
A. Aluminum Specimen
Mass of aluminum specimen M= 85.4g
Mass of calorimeter inner cup and stirrer Mc= 83.8g
Mass of calorimeter inner cup, stirrer, and water Mc+Mw= 322.7g
Mass of water Mw= 238.9g
Initial temperature of water Tc= 16.5°C
Initial temperature of aluminum specimen Tm= 100°C
Final temperature TF= 20.5°C

B. Copper Specimen
Mass of copper specimen M= 283.4g
Mass of calorimeter inner cup and stirrer Mc= 83.8g
Mass of calorimeter inner cup, stirrer, and water Mc+Mw= 330.9g
Mass of water Mw= 247.1g
Initial temperature of water Tc= 16.8°C
Initial temperature of copper specimen Tm= 100°C
Final temperature TF= 24.0°C

3.2 CALCULATION
A. Aluminum Specimen- cal calculation:
Mcal(Tm-TF)=MWcW(TF-TC)+MCcC(TF-TC)
𝑀𝑊𝑐𝑊(𝑇𝐹−𝑇𝑐)
cal= 𝑀(𝑇 −𝑇𝐹)−𝑀𝑐(𝑇𝐹−𝑇𝑐)
𝑚

238.9𝑔*1(20.5°𝐶−16.5°𝐶)
cal= 85.4𝑔(100°𝐶−20.5°𝐶)−83.8𝑔(20.5°𝐶−16.5°𝐶)
cal= 0.148 cal/g°C

B. Copper Specimen- ccu calculation:

Mccu(Tm-TF)=MWcW(TF-TC)+MCcC(TF-TC)
𝑀𝑊𝑐𝑊(𝑇𝐹−𝑇𝑐)
ccu= 𝑀(𝑇 −𝑇𝐹)−𝑀𝑐(𝑇𝐹−𝑇𝑐)
𝑚

247.1𝑔*1(24°𝐶−16.8°𝐶)
ccu= 283.4𝑔(100°𝐶−24°𝐶)−83.8𝑔(24°𝐶−16.8°𝐶)
ccu= 0.081 cal/g°C
4 ANALYSIS and DISCUSSION
To perform the analysis of this experiment, we used the formula to find the
specific heat of a metal specimen in a calorimeter (Formula 2). This allowed us
to understand the relationship between the mass, temperature and different
substances and how they correlate to the specific heat of said substance.

The calculation of both cal and ccu resulted in incorrect values. This was caused
by the assumed values of cW and the initial temperature of the aluminum specimen
Tm .The thermometer was not taken into account when creating the equation which
would also create errors with the results.

The objectives of this lab were to measure the specific heat of a metal
specimen using a calorimeter and to come to a deeper understanding of the
principle of conservation of energy as it applies to thermal energy. The first
objective was met throughout the performing of the experiment and the second
objective was met during the calculations where a better understanding of the
principle of conservation of energy was made while finding the value of cal and
ccu.

Lab Questions:
1. If the temperature of the sample were to cool down by 3°C the calculation
for aluminum would change from 0.148 cal/g°C to 0.154 cal/g°C. If the
temperature change was +- 0.2°C then the difference would be 0.140 cal/g°C
and 0.156 cal/g°C respectively.
2. If the specific heat of the calorimeter cup was off by 20% it would
drastically change the results. This difference changed the entire formula
currently used to solve for the specific heats of the copper and aluminum
specimens resulting in the entire mass and temperature difference being
used as the denominator causing an entirely different result.
3. If boiling water was carried over with the sample the final temperature
would be much higher. This is because more mass is being added to the
experiment then initially calculated.
4. If water splashed out of the calorimeter cup then the final temperature
would be lower due to the reduction of mass. But the condensation of the
water on the innercup does not affect the results since it is still being
accounted for through the measurement of its temperature.
 5. Having a lower starting temperature and higher ending temperature than the
room temperature for a calorimeter cup allows for a greater difference in
heat to be seen. This extreme difference to the room temperature allows it
to have less of an impact on the temperature change from initial to final.
6. The inclusion of the specific heat of the thermometer would cause the
specific heat of the specimens to be lower. This is because more
components are being added to the equation allowing for a more accurate
(and lower) value.
7. The error percentage of the aluminum specimen is 31% and the copper
specimen had an error percentage of 5%. As mentioned in the error analysis
the major source of error was in the calculation of the aluminum specimen
where the specific heat of water and the initial temperature of the
specimen were both assumed.

5 CONCLUSIONS
Throughout the experiment, we learned the connection between the specific heat
value of a metal (Aluminium and Copper) and the environment it's in. In this
experiment, the environment was a calorimeter filled with water. We also
learned how thermal energy transfers to other substances such as the water and
calorimeter through the calculations.

Some questions that were raised after performing the experiment were: What are
some real-world situations of heat transfer? Is there any system that uses heat
transfer as a power?

To improve the experiment and prevent further errors, the experiment should
include the measuring of the initial temperature of the metals and accounting
the thermometer into the calculations. With these changes the experiments in
the future will have more accurate results.
6 Attachment of Raw Data