LabReportSpecificHeatCapacity

Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Ciudad de México

International Baccalaureate Physics SL Lab Report: Specific Heat Capacity

Candidate names:

Katia Fernanda Albiter Vera Alan Galeana Vega Diego iego Mendi endiet etaa Ahuma humada da Diana iana Karen ren Tre Trejo Varga argass Dani Daniel el Vill Villan anue ueva va Rais Raisma man n

A01339936 A01339200 A0133 013393 9307 07 A0133 013395 9524 24 A013 A01339 3903 031 1

Session year: May 2017 Teacher’s name: Rogelio Oscar Caballero Pérez Lab Report: Specific Heat Capacity

Albiter, Galeana, Mendieta, Trejo, Villanueva

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Research Question:

How will different amounts of room temperature water in a closed system have an effect on the specific heat capacity of copper? Background Information:

When a given material is heated, its temperature increases in a certain amount depending on its physical and chemical properties. Every material has different responses to a given amount of heat energy due to its microscopic structure; this is a given quantity of heat energy will produce different temperature changes among different material. This capacity is called specific heat C and is measured in the following units: energy mass-1 temperature-1, and is commonly referred to as the energy needed to increase by 1 Kelvin the temperature of a 1 kg mass of the given substance, or the corresponding for other units. The specific heat depends only on the substance, independently of its geometry. Therefore, the increase in temperature of a material of mass m Q

when exposed to a heat energy transfer of Q will be ΔT = mC , with which we obtain the formula Q

for specific heat C = mΔT . (Hamper, 2014, 105 – 111) Measuring the specific heat capacity of materials can be done through various techniques: intuitively for a given substance mass we could measure the temperature increase as a function of supplied heat energy and obtain C in a straightforward manner. However, this requires the absolute measurement of the transferred heat, which is frequently difficult. An alternative technique consists of provoking the exchange of heat between the substance to be measured, and another reference material of known C r ; therefore, at the final equilibrium state, the absolute value of heat loss from one material equals the absolute heat gain by the other. In this case, only temperature measurements are necessary because the heat transfer is given by −mrC r ΔT r m sC s ΔT s = − mr C ΔT . We will measure r r , from which C s = m ΔT s can be obtained as C s s

ΔT r = T rf − T ri , and ΔT s = T sf − T si . Now, as in the final thermodynamical equilibrium T rf = T sf , we only need to measure three temperatures T si , T ri and T rf = T sf . This method assumes that there is no heat loss. Hence, we have to work in a somewhat isolated environment, trying not to wait too long before the measurements are recorded. Hypothesis:

In the closed system of the hot metal inside the room temperature water there would be a heat transfer from the metal to the water. When it reaches its final equilibrium state, the absolute value of heat loss from one material will equal the absolute heat gain by the other. The expected specific heat capacity for copper would be of 0.385 J g-1 K -1. (Keith Gibbs, 2013)


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Variables:

Table 1.1: Experimental variables and their impact Variables

Likely impact upon the investigation

How the variable will be changed/ measured/controlled

Independent variable Amount of water in

According to our hypothesis, the amount of water must not have an

The experiment will be performed ten times total, with three trials for

which the metal is submerged (mL)

impact on the specific heat capacity of the copper sample since it’s only one of its properties. If we use a small amount of water, its temperature raise will be high, and vice versa, maintaining the product mΔT = constant (CH2O= known constant).

100, 110, 120, 130, and 140 mL of water, which will be measured using the volume marks on the beakers. These values were chosen because they are small enough to allow for a significant temperature change which can be easily measured.

Although our final unknown quantity is the specific heat capacity of the copper sample, this will be estimated with the −mrC ΔT r r equation C s = m ΔT , where s stands s s

The change in the water temperature once the system stabilizes will be measured with the thermometer.

Dependent variable Change in water temperature (ºC) Specific heat for each water volume (ºC)

for the copper sample, and r for the water. Actually, the only variable we need is the final temperature of the combined system (water and copper sample), when the balance has been reached.


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Controlled variables Temperature of the

The initial temperature of the copper sample will determine the amount of

The initial temperature of the metal will be controlled by measuring the

metal after heating. Type of metal Mass of the metal

heat the water will absorb. The hotter it is, the higher temperature the water gets.

temperature with an infrared sensor. This value will be kept at 100ºC. We will only use copper in our

Each type of metal has an expected specific heat capacity that will have an influence on the experiment. The copper sample’s mass intervenes

experiment in order to obtain its specific heat capacity. We will use the same copper sample for all trials, in order to

in the equation since we have to measure it necessarily in order to obtain the specific heat.

maintain a constant mass.

Uncontrolled

Since we have limited time to perform

We will immediately place the

variables Time to

the experiment, we will not take into account the time needed for the system

copper sample into the water to minimize the amount of heat

to reach a temperature equilibrium. This shorter time means that the system might not reach a perfect equilibrium. We assume that there is no heat loss,

transferred to the environment. We will also wait an appropriate amount of time deemed necessary for the system to approach the

this is the total energy from the copper sample is transferred to the water; however, for longer settling times, some heat will be lost to the environment due to air currents and

equilibrium, which is when the ongoing change in temperature becomes negligible.

reach

equilibrium Heat loss

pressure, among others.

Apparatus:

● Copper sample ● Safety goggles ● Water (1200 mL) ● Hot plate ● Tweezers ● LabQuest Interface ● Temperature Sensor


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● 4 beakers of 200 mL ● Graduated cylinder Method:

1. Measure the mass of the 200 mL beaker. 2. Pour 100 mL of water into the 200 mL beaker and measure the new mass. 3. Measure the mass of the copper sample. 4. Introduce the thermometer in the beaker and write down the water’s temperature. 5. Turn the hot plate on and heat the copper sample until it arrives to a temperature of 100ºC measured with the temperature sensor. 6. Using the tweezers, grab the copper sample and drop it into the beaker. 7. With the help of the temperature sensor, watch for the change of temperature in the water. 8. Wait for the system to reach a temperature equilibrium, which is when the ongoing change in temperature becomes negligible, and measure the final temperature of the water. 9. Redo the experiment with 10 more mL of water in the beaker and stop when 140 mL are reached, making sure to perform two trials for each different amount of water. Figure 1.1: Experimental Setup


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Safety and Ethical Considerations:

This lab experiment has many possible hazards that can be reflected in the results we get. We will be careful in keeping the room temperature the same but if the clime changes as so does the temperature we will need to consider this as an uncontrollable variable caused by this environmental impact. We must also keep in mind that we are dealing with hot materials, boiling water and heated copper; hence, we must use the tweezers and be very careful to avoid any spilling of boiling water. A lab coat is essential in case of any accident that might occur with the hot water or apparatus that will be used. We also need to anticipate some sources of error in case metal we chose for our experiment does not give us the results that we need, perhaps because it was not what the team expected, then we will have other metals available just in case. The success in the lab can be measured easily as the specific heat of copper has been analyzed many times before so we will compare our results with the theoretical ones to see what our margin of error was and how we can improve. The social impact of our lab might not seem very straightforward but it can help prospective students see our methodology and results in order to improve them or take them into account. Analysis:

After retrieving the data of the experiment we made a table showing the change of the water volume, IV, its mass added to the mass of the beaker and the final and initial temperature in order to find out the change in temperature DV. Table 1.2: Data retrieved and organized of water volume, mass, initial and final temperature and change of temperature. Water volume (mL) ±1.0mL

Beaker No.

Beaker + Water Mass (g) ± 0.01g

Initial Temperature of the Water (ºC) ± 0.1ºC

Final Temperature (ºC) ± 0.1ºC

Change of Temperature Water (ºC) ± 0.2ºC

Change of Temperature Copper (ºC) ± 0.2ºC

100 mL

2

202.69

15.9

20.3

4.4

79.7

1

222.26

15.5

19.4

3.9

80.6

4

222.74

15.8

20.5

4.7

79.5

3

220.10

16.5

21.0

4.5

79.0

3

230.75

16.0

19.4

3.4

80.6

4

233.38

16.3

18.8

2.5

81.2

110 mL

120 mL


130 mL

140 mL

2

229.02

15.9

21.2

5.3

78.8

1

251.58

16.3

19.6

3.3

80.4

1

259.91

16.1

19.8

3.7

80.2

2

239.49

16.1

19.9

3.8

80.1

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Then a graph was produced with the data collected and the calculated change of temperature in which we saw how the values we got were very close and did not seem to be proportional on the graph. As the scale of the mass of water was big the uncertainties on the x axis were negligible and did not appear in the graph while the uncertainties in y axis were considerable but still very small. Graph 1.1: Change of Temperature vs Mass of Water

In this case calculations will be required to determine the specific heat capacity of copper. For this, the specific heat capacity of water was required which is 4.186 JK -1(Keith Gibbs, 2013). The mass and the change of temperature calculated before were also necessary to determine the amount of energy that the mass of water gained. By reference on the law of conservation of energy we know that the sum of the total energy in an isolated system will remain constant as this energy isn't lost but transferred from one body to another. Based on this, we are able to deduce that the caloric energy that the water gained was transferred from the copper, in other words the copper lost the same joules the water gained as energy is conserved. We also know that by the zero law of thermodynamics


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To calculate the specific heat of copper, we first used the specific heat of water, the mass and the change of temperature to calculate the amount of energy that the mass of water gained. Basing ourselves on the law of conservation of energy, we know that energy cannot be created, only transferred and transformed. Using that knowledge, we can deduce that the caloric energy gained by the water came from the copper, in other words, the copper lost the same joules the water gained. Because of the Zeroth Law of thermodynamics, we know that the final temperature of water is the same as the final temperature of copper when both are in thermal equilibrium. Then by knowing the mass of copper and having calculated the change in temperature and the energy that it represents. We can apply the following formula ( Mc)(ΔT c)(C c) =J or (mass of copper)(change in temperature)(specific heat capacity)= Energy, to solve for (C c) and know that by dividing the energy by the product of the mass and the change of temperature we get the specific heat capacity of the copper. We also used this formula with the quantities of water so we could equal the energy and produce only one formula that would give us the specific heat capacity of our trials. ( M w)(ΔT w)(C w) = J and ( M c)(ΔT c)(C c )= J then ( M c)(ΔT c)(C c) = ( M w )(ΔT w )(C w ) M c: Mass of copper

ΔT c : Change of temperature copper

C c : Specific heat capacity copper

M w: Mass of water plus

ΔT w : Change of temperature water

C w : Specific heat capacity water

Specific heat capacity of water = 4.186 J K -1 (Keith Gibbs, 2013) Mass Cu = 58.13 g ± 0.01g The table below shows the average of the amount of water, change of temperature of water from table 1.1. With this and the specific heat capacity of water the total energy transfer was calculated by using the formula ( Mw)(ΔT w)(C w )= J. Then the change of temperature of the copper was determined by subtracting the final temperature of the water to a 100 C° which is the temperature in which water boils. With this values we could use the formula stated above of ( Mc)(ΔT c)(C c) = ( Mw)(ΔT c)(C w ) to get the specific heat capacity of copper and average the results in order to eliminate random errors and get as close as possible to the expected value. Table 1.3: Average amount of amount of water, change of temperature in water and in copper and specific heat capacity of copper .


Water (g) ± 0.02 g

ΔT water (C°) ± 0.2°

Total energy transfer ± 0.22 J

ΔT Cu (C°) ± 0.2°

(C p) ± 0.3Jg-1K -1

98.31

4.15

1707.8 J

80.15

0.37

106.81

4.60

2056.7 J

79.25

0.45

116.62

2.95

1440.1 J

80.90

0.31

126.14

4.30

2270.5 J

79.60

0.49

135.54

3.75

2127.6 J

80.15

0.46

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Average C c = 0.416 ± 0.09 J g-1 K -1 We thus get the average of the column of specific heat capacity and we determine that the specific heat capacity of copper is of 0.416 ± 0.09 J g-1 K -1. Conclusion:

In our experiment, we observed how the temperature change of water (DV) varied for different initial values of the water volume. We expected that this change should decrease as the volume of water increased so that the specific heat of copper should remain constant as the theory states. However, in our experiment we obtained some deviations in the expected temperature change, as shown in Table 1.3, where we present the values of the calculated specific heat capacities for each variable change. There was a considerable variation among these values, which means that our measurements were slightly imprecise. Albeit, when calculating the average of these values, we obtain a specific heat capacity of copper of 0.416 ± 0.09 J g-1 K -1 (without taking into account significant figures) which, given the experimental uncertainties, is close to the theoretical value of 0.385 J g-1 K -1, exhibiting an experimental error of 8%, thus deeming our results reasonably accurate. Evaluation, improvements and next steps:

Table 1.4: Evaluation of experimental errors Weakness/Source of error

Possible effect on data and Suggested improvement magnitude of weakness/error

Independent variable:

●

The water measurements done In order to increase the accuracy

The amount of water in with the graduated cylinder had in the water volume which the metal was an uncertainty of 1 milliliter, but measurements, we could use a going to be submerged while pouring the water inside,


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was measured with a the water started forming some shallower container, such as a graduated cylinder, an bubbles due to its fall into the smaller glass graduated cylinder. instrument that leaves a container, which might have very small uncertainty.

affected the measurement more than expected.

The total energy transfer had an The change of uncertainty of 0.2ºC, which temperature in the water means the instrument was was measured with a adequate to measure the water

In order to minimize that 8% error ratio, we could use water that had the same temperature or with a minimum difference

LabQuest Interface, which is a reasonably accurate system and has little uncertainty. The specific heat for each water volume didn’t was not consistent with the

throughout the different samples. Besides this, the LabQuest Interface continually kept showing changes in the copper sample’s temperature. This meant the measurements were not accurate and this can be

Dependent variable

●

●

temperature. The collected data showed us that there is a variation in the copper’s specific heat depending on the water’s volume with an experimental error of 8% compared to the theoretical value.

expected results since they did present a small variation but our specific heat calculations were accurate.

improved by using other heat calculating instruments, like an infrared sensor with a bigger ratio than the one we first planned on using.

The copper sample’s temperature We could improve the precision The temperature of the change had an uncertainty of of the experiment by reducing the metal after heating was 0.2°C, but it might have also transition length between the hot

Control variables

●

presented a variation on the total energy transfer from the metal to the water. Besides this, the air currents and the temperature of the environment might have slightly affected the data while measuring with the LabQuest Interface.

plate and the beaker (this will lower the temperature variation ratio) and use another instrument to measure the sample’s temperature, like an RTD., that has an average uncertainty of only 0.03ºC. We could also isolate the system more effectively using appropriate containers.

The experiment had minimum ● The heat loss from the variations when calculating the moment the copper was specific heat capacity, since the removed from the hot collected data has a different plate and dropped into magnitude than the expected the water beaker. theoretical value.

As an improvement a faster process when taking the copper from the hot plate into the water would decrease our errors. The air conditions can not be controlled in the lab, but the experiment could be done,

●

not properly measured since there’s always a heat loss when the object moves. This happened when putting it into the water beaker. The type of metal had no variation whatsoever and neither did its mass.

Uncontrolled errors


●

The

lab’s temperature

instead, in a vacuum chamber

and air currents influenced the copper sample’s measurements.

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and it will be more accurate.

heat

Some heat from the copper We could suspend the copper ● The contact of the copper sample was transferred to the sample from a string so that there sample with the glass beaker instead of the water itself, is no point of contact with the beaker was unregulated. thus being another source for beaker. This could also help

Qualitative Data

●

The copper sample made unmeasured heat loss to the contact with the table environment. Furthermore, in accidentally. some cases the tweezers didn’t provide a stable handle on the copper sample, which provoked its accidental drop on the table, and although we recovered it immediately, it did provoke, once again, an unmeasured heat loss.

lifting the sample from the hot plate since it would provide a better support than the tweezers we originally used.


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References:

Hamper, C. (2014). Standard Level Physics (2nd ed.). Essex: Pearson. Keith Gibbs. (2013). “Heat Energy”. School Physics. Retrieved February 16, 2016, from: http://www.schoolphysics.co.uk/age14-16/Heat%20energy/Heat%20energy/text/Specific_heat_c apacity_and_heat_energy/index.html

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