physics lab report

specific heat of solids

1. Introduction

Heat capacity of a body is the quantity of heat required to raise the temperature of the body by 1oC. The specific heat of a substance is the heat capacity per unit mass. Thus, heat capacity = mass x specific heat. The specific heat is essentially a measure of how thermally insensitive a substance is to the addition of energy. Heat and temperature are really different quantities. Heat is a quantity of thermal energy, while temperature determines the direction and rate of heat transfer to the surroundings. It is possible for an object to have a very high temperature but contain very little heat and vice versa (physics 312).

When a hot body is mixed with the cold body, the hot body cools down and the cold body warms up until the mixture as a whole comes to a common temperature, that is, in thermal equilibrium. By mixing hot and cold substances and measuring the change in temperature, the thermal characteristics of the substance can be determined. The purpose of this experiment is to understand the difference between heat and temperature, and make some quantitative measurements concerning both. We used the technique called calorimetry to measure the specific heat. Calorimetry, it is the process of measuring quantities of heat. The purpose of the calorimeter is to prevent heat lose to the surroundings (Leybold 2000).

Calorimetry is literary “the measurement of heat content”. In this experiment, a certain amount of hot water, at a particular temperature, is poured into the calorimeter containing tap water of known mass and initial temperature (Hubsch, 2001). The equilibrium temperature is then measured and the mass of the whole mixture is measured. For part B, solid specimen shots of known mass were mixed with the tap water of known temperature in the calorimeter and a certain amount of hot water of known temperature is added.

The equilibrium temperature is then measured and the mass. By measuring and gathering the correct temperature and heat we were able to determined the heat capacity of the calorimeter and the specific heat of certain solid specimens, which is the objective of the experiment.

2. Theory

Heat is a form of energy. It is expressed either in joules (J), calories (cal), or kilo-calories (kcal). The change in thermal energy of an object is proportional to the change in its temperature. The method of mixtures makes use of the principles that when two bodies at different temperatures exchange heat, the quantity of heat lost by the warmer body is equal to the heat gained by the cooler body, and some intermediate equilibrium temperature is finally reached. This is true provided no heat is lost or gained from/to the surroundings. The different bodies require different amounts of heat to raise their temperature by one degree (Venable, 2000).

This amount of heat is called the heat capacity, C, of the body. The heat capacity C of an object is defined as,

C = ∆Q/∆T [1]

where ∆Q is the amount of heat required to change the temperature of the object by ∆T. The specific heat capacity, c of a substance is the heat capacity per unit mass.In mathematical form,

C= ∆Q/m∆T [2] where c is the specific heat in Joule/kg ● Co, ∆Q is the amount of heat in Joules, m is the mass of the substance in kg, and ∆T is the change in temperature in Co (Physics 31 lab). In measuring c, the bodies are placed in a container where the heat exchange takes place. It is called a calorimeter. A calorimeter, is an object used for calorimetry. It is composed of an outer vessel and an inner vessel separated by an insulating layer. Seen in figure 1, are the parts of the calorimeter.

Figure 1. The parts of a calorimeter

From the figure above the calorimeter consists of six (6) parts which is, the inner vessel, outer vessel, thermometer, stirrer, insulating cover, and the holes. For the first part of the of the experiment, heat capacity Cc of the calorimeter was determined by mixing hot and cold water. The equation for heat exchange is given by,

Heat lost by hot water = heat gained by cold water and calorimeter

-mhwCw ∆Thw = mcwCw ∆Tcw + cc ∆Tc [3]

-mhwCw (T3-T1) = mcwCw (T3-T2) + Cc (T3-T2) [4]

Where mhw = mass of hot water mcw = mass of cold water
Cw = specific heat of water = 4190 J/Kg●C0
Cc = heat capacity of calorimeter including the stirrer and thermometer
T 1 = initial temperature of hot water
T 2 = initial temperature of cold water and calorimeter
T 3 = final or equilibrium temperature of the system

For part B of the experiment, the specific heat of a solid was determined by measuring the heat lost and gained in the heat exchange between the two bodies which is the solid substance and the mass of water. The solid specimen of known mass was mixed with the tap water of known temperature in the calorimeter. A certain amount of hot water was added into the mixture. After mixing, the system comes to a common equilibrium temperature and was measured. The equation of heat exchange is given as,

Heat lost by hot water = heat gained by metal shots, tap water and calorimeter

-mhwCw ∆Thw = msCs∆Ts + mcwCw ∆Tcw + Cc ∆Tc [5]

-mhwCw (T6-T4) = msCs(T6-T5)+ mcwCw (T6-T5) + Cc (T6-T5) [6]

Where mhw = mass of hot water ms = mass of metal shots mcw = mass of cold water
Cw = specific heat of water = 4190 J/Kg●C0
Cs = specific heat of metal shots
Cc = heat capacity of calorimeter including the stirrer and thermometer
T 4 = initial temperature of hot water
T 5 = initial temperature of the metal shots, cold water and calorimeter
T 6 = final or equilibrium temperature of the system

From equation (5), the specific heat of the metal shots can be computed.

3. Methodology

From the experiment, we determined the heat capacity of the calorimeter by mixing cold and hot water. A certain amount of hot water was poured into the calorimeter containing tap water of known mass and initial temperature. The mixture was stirred until the system comes to a common equilibrium temperature. For part (a) of the experiment a water was boiled on the boiler using a Bunsen burner then, the inner vessel was taken out of the calorimeter and dried if it is wet. A 100 ml of tap water was prepared in a beaker afterwards. The inner vessel was measured on the digital platform balance and its mass was recorded. Then, the 100 ml water that we prepared was poured into the inner vessel and measured the total mass of the inner vessel and its content. Then, the inner vessel with its content was placed back into the calorimeter, covered it with the lid and stirred. Then, the temperature was recorded after the reading of the thermometer stabilized.

Afterward, we prepared 100 ml of hot water in the beaker. The temperature of the hot water was recorded and was poured immediately into the calorimeter. The calorimeter was covered immediately. We stirred the mixture until the equilibrium temperature was reached and record the temperature that we gathered. Afterwards, the mass of the inner vessel and the mixture was measured. From this value we calculated the mass of the hot water that was poured into the mixture. After calculating the mass of the hot water , the heat capacity of the calorimeter, Cc, was computed. Then, the calorimeter was disassembled, we prepared the materials again and the steps was repeated for the second trial. After gathering all the needed data, the average and the Mean Absolute Deviation (MAD) of the computed values was computed.

For part (b) of the experiment the specific heat of a solid sample were to be determined. Solid specimen shots of known mass were mixed with tap water of known temperature into the calorimeter. First we followed the first procedure, the inner vessel was taken out of the calorimeter then the empty inner vessel was placed on the digital platform balance measured and recorded its mass. Then, the metal shots was placed into the vessel, we measured and recorded its total mass. afterwards, the inner vessel was added with 100 ml of tap water enough to immersed the metal shots and the total mass was recorded.

The inner vessel together with its content was placed back into the calorimeter, covered with its lid and stirred it. The temperature was then recorded after the reading of the thermometer stabilized. A 100 ml of hot water was prepared in the beaker and was poured immediately into the calorimeter. The calorimeter was covered immediately. The mixture was stirred until the system comes to a common equilibrium temperature then the temperature was recorded. Afterwards the mass of the inner vessel and the mixture was measured and from this value, the mass of the hot water that was poured into the mixture was calculated. The specific heat of the metal shots ,Cs, was computes using the value of the heat capacity, Cc, of the calorimeter obtained in part (a). Then, the materials was prepared again for the second trial. The average and the Mean Absolute Deviation (MAD) was determined using the values that we gathered.

4. Results and Discussion

Table 1. Determination of the heat capacity of the calorimeter

1st
2nd
Unit
Mass of inner vessel

0.04494
0.04492
Kg
Mass of cold/tap water mcw 0.08704
0.08494
Kg
Mass of inner vessel + cold water + hot water

0.2134
0.2134
Kg
Mass of hot water mhw 0.08142
0.08353
Kg
Initial temperature of hot water
T1
71.0
70.0
0C
Initial temperature of cold water & calorimeter
T2
29.0
27.0
0C
Final/equilibrium temperature of the system
T3
47.0
46.0
0C
Specific heat of water
Cw
4190
J/Kg●C0
Heat capacity of calorimeter + stirrer + thermometer
Cc
90.17
86.19
J/Kg●C0
Average heat capacity of calorimeter

88.18

Error in the heat capacity (MAD)

1.99

From the table above, we can see the different values that we have gathered during the experiment. As, shown from our first trial the value of the mass, of the inner vessel is almost the same with the value of the second trial there was only very little difference. The same with the values in the mass of cold/tap water there was only very slight difference. For the mass of the inner vessel mixed with the hot and cold water the first and second trial were the same. In the mass of hot water, it was not measured by the platform balance so it was calculated through adding the mass of the inner vessel and tap water then subtracted with the mass of inner vessel mixed with the hot and cold water.

We obtained the mass of the hot water and there was slight difference with the value in the first and second trial. For the initial temperature of hot water the difference was only one degree. Same with the final/equilibrium temperature of the system the difference was also one degree. In the initial temperature of cold water and calorimeter three degrees was the difference. And there is only one constant value from the table the specific heat of water which is 4190 J/Kg●C0.

Next was to determined the heat capacity of the calorimeter together with the stirrer and thermometer which was the objective of the experiment. From the equation (4), we substituted the gathered values and determined the heat capacity for the first trial and the second trial. There was a difference between the two values they were quite far, but not that far from each other. From the value of heat capacity of the first and second trial we were able to determine the average heat capacity, which is 88.18. And from that, we were able to determine the Mean Absolute Deviation (MAD) or the error in the heat capacity, which is 1.99.

Table 2. Determination of the specific heat of the metal shots

1st trial
2nd trial
Unit
Mass of inner vessel

0.04490
0.04491
Kg
Mass of inner vessel + metal shots

0.2423
0.2422
Kg
Mass of inner vessel + metal shots + cold water

0.3219
0.3213
Kg
Mass of inner vessel + metal shots + cold water + hot water

0.3995
0.3985
Kg
Mass of metal shots ms 0.1974
0.1973
Kg
Mass of cold/tap water mcw 0.07959
0.07909
Kg
Mass of hot water mhw 0.07763
0.07723
Kg
Initial temperature of hot water
T4
71.0
74.00
0C
Initial temperature of cold water + metal shots + calorimeter
T5
27.0
26.0
0C
Final/equilibrium temperature of the system
T6
46.0
47.0
0C
Specific heat of water
Cw
4190
J/Kg●C0
Heat capacity of calorimeter + stirrer + thermometer
Cc
94.50
84.66
J/Kg●C0
Specific heat of metal shots
Cs
2.03x10-3
9.85x10-3
J/Kg●C0
Average specific heat of metal shots

5.94x10-3

Error in the specific heat (MAD)

3.91x10-3

Kind of material metal shots are made of
Fe
Iron

Accepted value of the specific heat of the metal
Cc
4.0x10-3/.444 J/kg●C0

In table (2), it is different from table (1) because on table 2 we are going to determine the specific heat of the metal shots that was given in each group, and our metal shots was Iron (Fe). From the table shown above we were tasked to determine the value of the mass of the inner vessel [1], inner vessel with metal shots[2], inner vessel mixed with metal shots and cold water[3], inner vessel together with the metal shots, cold water and hot water[4], mass of metal shots[5], mass of cold water[6] and lastly mass of hot water[7].

The each values of mass in the 1st and 2nd trial slightly differ from one another, they differ in a few points only. For the mass of the cold water we determined its value by subtracting the mass of the inner vessel with the metal shots with the mass of the inner vessel mixed with the metal shots and cold water. For the mass of the metal shots we determined its value by adding the mass of cold water, hot water and inner vessel then subtracted with the inner vessel mixed with the metals shots, cold and hot water. The values gathered from the experiment are almost the same, there is one constant value that was given in the experiment and it is the value of specific heat of water which is 4190 J/kg●C0. In this part we were ask to determine the heat capacity of calorimeter with the stirrer and thermometer, using equation (4) we were able to determine the heat capacity.

The heat capacity in table (1) are almost the same but with only little difference. With the heat capacity we can now determine the specific heat of the metal shot, using equation (6) we substitute the gathered values and obtained the value for the specific heat of metal shots. The value of Cs, in the first trial differs a lot from the Cs, in trial two. The value of Cs, in the first trial is 2.03x10-3 and the Cs, in trial two is 9.85x10-3. From the specific heat , we can determine its average which is 5.94x10-3 and we can also determine the Mean Absolute Deviation (MAD), which is 3.91x10-3. the error in the specific heat is not so different with the accepted value of the specific heat of Iron (Fe) which is 4.0x10-3/.444.

5. Conclusion

In this experiment our tasks was to be able to determined the heat capacity of a calorimeter and the specific heat of certain solid specimens. Our experiment was successful we were able to preform and finish the experiment, gather what was needed to be gathered and compute what was needed to to compute. The first objective was to determine the heat capacity in determining the heat capacity we are going to use equation (4) which is,
-mhwCw (T3-T1) = mcwCw (T3-T2) + Cc (T3-T2)

When, we gathered the values we simply substituted its corresponding value to the equation and determine the heat capacity (Cc), shown in table 1 were the values and our heat capacity of calorimeter in the first trial was 90.17 J/kg●C0 and for the second trial it was, 86.19 J/kg●C0. We have computed the correct heat capacity because the heat capacity should be around 50-90 J/kg●C0. From heat capacity we can also determine its average by adding the two heat capacity and divide them by two.

Its average was 88.18 J/kg●C0.. The error in the heat capacity (MAD) was also determined. Its error was 1.99. The second objective was to determine the specific heat of a solid sample. Our solid sample was Iron (Fe). After the part A of the experiment we gathered the second values for our table 2 and in determining our specific heat we are going to use equation (6) which is,

-mhwCw (T6-T4) = msCs(T6-T5)+ mcwCw (T6-T5) + Cc (T6-T5)

After gathering all the needed values just like in part A, we substitute the corresponding value to the equation given, and we can determine the specific heat of the solid specimen, for the first trial the specific heat (Cs), was 2.03x10-3 and for the second trial the specific heat (Cs), was 9.85x10-3. The average specific heat was also determined by adding the two specific heat and dividing then by two, its average was 5.94x10-3.. The error in the specific heat (MAD) was calculated and was compared to the accepted value of the specific heat of the metal. Its error was 3.91x10-3 the accepted value was 4.0x10-3/.444.

6. References

BOOKS:

[1] Howard, P. G.,(1986). Physics (2nd ed.). San Francisco: Pearson education. (pp. 56-58).

[2] Pettingill, M.S., Jr. (1980). Heat. The world bool encyclopedia. (vol. 9, pp 134-136). Chicago: World Book.

INTERNET:

[3] Fitzpatrick, R. C.,(2006). Specific heat of solids. Physics. Retrieved September 28, 2013, from http://farside.ph.utexas.edu/teaching/sm1/lectures/node71.html [4] Durham University. Heat capacity of physics. Department of Physics. Retrieved September 28, 2013, from http://labs.physics.dur.ac.uk/level3/CMP/scripts/12_10_10_Heat_capacity_of_ solids.pdf [5] Kamal, P. R.,(2000). Heats. Physics. Retrieved September 29, 2013, from http://www.physics1.howard.edu/specific_Heat.com [6] St. Louis Community college. Specific Heat. Retrieved September 29,2013, from http://users.stlcc.edu/dedmonds/Labs/pdfs/specificheat.pdf

[7] young, E. D. (1989). Modern physics. Retrieved September 30, 2013, from http://pec.sjtu.edu.cn/ols/P2/P2321_E.com

References: [2] Pettingill, M.S., Jr. (1980). Heat. The world bool encyclopedia. (vol. 9, pp 134-136). Chicago: World Book. [7] young, E. D. (1989). Modern physics. Retrieved September 30, 2013, from http://pec.sjtu.edu.cn/ols/P2/P2321_E.com