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Specific heat of solids

The objective of the study is to explain, measure and better understand the specific heat of copper and lead using the method of mixtures. Heat is a form of energy it is either expressed in joules, calories, or kilo-calories According to the law formulated by the French chemists Pierre Louis Dulong and Alexis Thérèse Petit, the specific heat of solids which is characterized as the amount of heat required to raise the temperature of one gram of a substance to one degree Celsius specimens are inversely proportional to their atomic weights; that is, the specific heat multiplied by the atomic weight is approximately a constant quantity for all the solid elements. ( The heat capacity C of an object is defined as c= Q/m?T, where Q is the amount of heat required to change the temperature of the object by T. The specific heat c of a substance is the heat capacity per unit mass. The specific heat is measured in J/kgoC or cal/goC or kcal/kgoC. Suppose we have two objects, one hot and one cold. Let m1 and m2 be the masses of the hot and cold objects,T1 and T2 be the temperatures of the hot and cold objects, and c1 and c2 be their specific heats respectively. These two objects are brought into thermal contact with each other and allowed to reach a common final equilibrium temperature T3. We are assuming the system to be thermally insulated from the surroundings. According to conservation of energy, the heat gained by the cold object would equal the heat lost by the hot object.
?Qgained = ?Qlost;
m2c2 (T3 - T2) =m1c1 (T1 ? T3)
For this experiment, consider your system to consist of mixing a given mass m1 of a ?hot" specimen with specific heat c1 at temperature T1 and a known mass m2 of water with specific heat c2 at a lower temperature T2 contained in a calorimeter of mass m3 with specific heat c3 also initially at temperature T2. Once again, we assume the system to be thermally insulated from the surroundings, and the heat capacity of the thermometer, which records the temperature, can be neglected. Let the final temperature of the mixture be T3. Energy conservation gives:
Qlost(specimen) = Qgained(Water) + Qgained(Calorimeter)

which yields the unknown specific heat c1 of the specimen as
c1 = (m2c2+m3c3) (T3 - T2)
m1(T1 ? T3)
We assume that the mixing can be done without loss of heat by the hot specimen to the surroundings.
We will consider a specimen heated to a high temperature is dropped into water contained in a calorimeter cup at a lower temperature. If this system is thermally insulated from the surroundings, the specific heat of the specimen can be determined by equating the heat lost by the metal to the heat gained by both the calorimeter cup and the water contained in it. ( )

III. Diagram/Materials

IV. Procedure

The initial masses of boiler dipper, copper, lead, dipper and shots, inner vessel with water, and water are measured and recorded. The specimens (copper/lead) are heated and the initial temperatures are recorded after which, it is dropped in the calorimeter containing cold water. The temperature rise of the water in the calorimeter is observed and recorded. From the data gathered, the specific heat of the specimen can be known through the formula stated above.

V. Data

Material of Specimen Lead Copper
Mass of Boiler Dipper, m1(gm) 85 85
Mass of Dipper and Shots,m2 (gm) 320 280
Mass of shots,ms=m2-m1 (gm) 235 195
Mass of inner vessel w/ water,m3 (gm) 220 220
Mass of water, mw=m3-mc (gm) 165 165
Temperature of hot shots,T1 (oC) 83 84
Initial Temperature of System, T2 (oC) 22 21
Final temperature of system,T3 (oC) 26 26
Specific heat of water,cw (cal/gmoC) 1.00 1.00
Specific heat of specimen,cw (cal/gmoC)(Experimental) 0.052 0.072
Specific heat of specimen (cal/gmoc) (standard) 0.036 0.092
Percentage Error 44.4% 21.7%

VI. Sample Computation
c= Q/m?T
Qlost(specimen) = Qgained(Water) + Qgained(Calorimeter)

cs = (mwcw+mccc) (T3 - T2)
ms(T1 ? T3)
cs = ((1)(165)+(0.215)(55))(26-21)

195 (84-26)
11310 cs = 825 + 59.125
= 0.072 cal/gCo

% ERROR = / Standard ? Experimental/ x 100%


= /0.072-0.092/ x 100%
= 21.7%

VII. Analysis

Based on the data above, I can say that the specific heat of material differ depending on the kind of substance. The specific heat for copper for example, after the experiment, became 0.052 cal/gmoC while on the other hand; the lead?s specific heat became 0.072 cal/gmoC. The 2 solids have achieved different results even though the procedure done for both was the same. This is because the different specimens differ in tolerance when heat is concerned. Therefore, the required amount of heat needed to change the temperature of a unit mass of substance by one degree also varies.

Although the method mixture is an effective way to measure the specific heat of a given specimen, it is not entirely accurate. The errors in the experiment were primarily due to outside factors such as the wind, weather, etc. Also, the stirrer of the calorimeter added to the mass of the calorimeter which provided inaccuracy in measurement.

VIII. Conclusion
In conclusion, I can say that the method of mixtures is a simple but an effective way to compute for the specific heat of specimens. In addition, the experiment helped clarify the concept of specific heat. I have learned that the specific heat is the amount of heat required by an object for it to change its temperature by a certain amount usually by one degree. This was shown when the specimens were transferred from one container to another that differed in temperature.

IX. Answer to questions

1. The thermometer also gains some of the heat. Neglecting the heat capacity of the thermometer, it causes inaccuracy in the measurement of specific heat.

4. given:
Ms = 50 g
T1 = 100 C
Mw = 200 g
T2 = 20 C
Cc = 0.092
Mc = 100
T3 = 22

Cs = ((200)(1)+(100)(0.092))(22-20))


Cs = 0.107 cal/gCo

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