MAPUA INSTITUTE OF TECHNOLOGY

Department of Physics

E302: HEAT AND CALORIMETRY GICALE, PATRICK EMMANUEL T.

gicalep@gmail.com/2014106318/CE-2

PHY12L-B2 Group 2

17 May, 2016

SCORE

Signed Data Sheet (5)

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Observations & Results (15)

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Graphs (10)

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Conclusion (15) = ____

References (5)

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Photos (10) = ____

Performance (40)

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TOTAL (100)

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E302: HEAT AND CALORIMETRY

Gicale, Patrick Emmanuel T.1, 1 School of Civil, Environmental, and Geological Engineering, Mapúa Institute of Technology

658 Muralla St., Intramuros, Manila City, Philippines

gicalep@gmail.com

OBSERVATIONS AND RESULTS

Materials possess, it may be a solid, liquid or a gas, a specific amount of heat, which differs from

all of the bodies also relative to its size, needed to be absorb to raise its temperature and this is

Specific Heat.

In our experiment, we are tasked to determine the metal samples’, aluminium and copper, specific

heat capacity through the formula of sensible heat.

𝑸 = 𝒎𝒄∆𝑻 (1)

The second part of the experiment is the determination of the latent heat of fusion of ice. It is a

constant which will dictates the needed heat to be absorb or taken off. Latent Heat of fusion is solve

through the formula.

𝑸 = 𝒎𝑳𝒇 (2) After doing two trials of determining the specific heat capacity of the two metals, we achieved a

relevant specific heat capacity. Below are the relevant values that we’ve gathered.

Table 1: Data Gathered for Determining the Specific Heat of Metals

Aluminium metal Copper metal

Mass of metal (g) 32.7 19.6

Mass of calorimeter (g) 46.3 46.3

Mass of water (g) 127.1 133.3

Initial temperature of metal (oC) 100 100

Initial temperature of calorimeter (oC) 26 27

Initial temperature of water (oC) 26 27

Final temperature of mixture (oC) 30 28

Experimental specific heat of metal

(cal/g-Co)

0.2397 0.1016

Actual specific heat of metal (cal/g-

Co)

0.2174 0.0932

Percentage of error 10.26% 9.0035%

As you can see, the following metals have different specific heat where aluminium being the

greater. Hence, the aluminium metal needed greater heat than the copper to raise its temperature.

Below were represents the data gathered to determine the ice’s latent heat of fusion and as you

can see, the experimental values have a minimal deficiency to its actual value. Sources of error

will be discussed on the conclusion.

Table 2: Data Gathered to Determine the Latent Heat of Fusion of Ice

1st Trial 2nd Trial

Mass of calorimeter (g) 46.3 46.3

Mass of water (g) 114.3 139.2

Mass of mixture (g) 160.3 167.6

Mass of ice (g) 46.3 46.3

Initial temperature of ice (oC) 0 0

Initial temperature of calorimeter (oC) 62 65

Initial temperature of water (oC) 62 65

Final temperature of mixture (oC) 19 34

Experimental latent heat of fusion

(cal/g)

96.5015 65.9403

Actual specific latent heat of fusion

(cal/g)

80 80

Percentage of error 20.63 % 17.57 %

Below is a sample computation for solving the specific heat.

𝑚𝑐𝑐𝑐∆𝑡𝑐 + 𝑚𝑤𝑐𝑤∆𝑡𝑤 + 𝑚𝑚𝑐𝑚∆𝑡𝑚 = 0

Aluminium metal:

(46.3𝑔) (0.2174𝑐𝑎𝑙

𝑔𝐶𝑜) (30 − 26)𝐶𝑜 +

(127.1𝑔) (1𝑐𝑎𝑙

𝑔𝐶𝑜 ) (30 − 26)𝐶𝑜 +

(32.7𝑔)𝑐𝑚(30 − 100)𝐶𝑜 = 0

cm=0.2397 cal/g-Co

𝒄𝒎(𝒂𝒄𝒕𝒖𝒂𝒍) = 𝟎. 𝟐𝟏𝟕𝟒𝒄𝒂𝒍

𝒈− 𝑪𝒐

% 𝑒𝑟𝑟𝑜𝑟

= |0.2174

𝑐𝑎𝑙𝑔𝐶𝑜 − 0.2397𝑐𝑎𝑙/𝑔𝐶𝑜

0.2174 𝑐𝑎𝑙/𝑔𝐶𝑜| 𝑥100

% 𝒆𝒓𝒓𝒐𝒓 = 𝟏𝟎. 𝟐𝟔%

Copper metal:

(46.3𝑔) (0.0932𝑐𝑎𝑙

𝑔𝐶𝑜) (28 − 27)𝐶𝑜 +

(133.3𝑔) (1𝑐𝑎𝑙

𝑔𝐶𝑜 ) (28 − 27)𝐶𝑜 +

(19.6𝑔)𝑐𝑚(28 − 100)𝐶𝑜 = 0

cm=0.1016 cal/g-Co

% 𝑒𝑟𝑟𝑜𝑟

= |0.0932

𝑐𝑎𝑙𝑔𝐶𝑜 − 0.1016𝑐𝑎𝑙/𝑔𝐶𝑜

0.0932 𝑐𝑎𝑙/𝑔𝐶𝑜| 𝑥100

% 𝒆𝒓𝒓𝒐𝒓 = 𝟗. 𝟎𝟎𝟑𝟓%

Sample Computation for solving Latent Heat of Fusion of ice:

𝑚𝑤𝑐𝑤(𝑡𝑚𝑖𝑥 − 𝑡𝑤) + 𝑚𝑐𝑐𝑐(𝑡𝑚𝑖𝑥 − 𝑡𝑐) + 𝑚𝑖𝑐𝑒𝐿𝐹 + 𝑚𝑖𝑐𝑒𝑐𝑤(𝑡𝑚𝑖𝑥 − 0) = 0

(114.3𝑔) (1𝑐𝑎𝑙

𝑔𝐶𝑜) (19 − 62)𝐶𝑜 + (46.3𝑔)(0.2174

𝑐𝑎𝑙

𝑔𝐶𝑜)(19 − 62)𝐶𝑜 + (46.3𝑔)𝐿𝐹 +

(46.3𝑔)(19 − 0)𝐶𝑜 = 0

LF=96.5015

GRAPHS

The table below represents the comparison of the relevant values that we’ve gathered to the

actual value. As you can see, Aluminum metal has greater specific heat capacity thus, the metal

needs greater heat to raise its temperature.

The table below represents the difference of the experimental value from the actual value. As

you can see, the following experimental data are close to the actual value.

CONCLUSIONS

Objectively, we've solved the metals’ specific heat and the ice’s latent heat of fusion. Comparing

the experimental data to the actual values, the percentage error from the first part are 10.26%

(Aluminum) and 9.0035% (Copper). Hence, the data gathered is acceptable. Next part, the

comparison from the experimental values to the actual values are somehow big. The percentage

error is 20.63% and 17.57%. Possible source of these big errors might be the initial temperature of

the water. Since, the environment is cold and heat travels from hot to cold thus, we can say that

the ice didn't melt. Thus, the final temperature of the mixture might not be accurate. To improve

the data, the experiment must be done in a normal room temperature.

Based on the data, specific heat capacity is relative to its mass and the heat transferred. As to the

data, since the change of the temperature of calorimeter and water of the aluminium is greater than

the copper hence the heat transferred is greater than the mass. Thus, aluminium’s specific heat is

still greater. As to the latent heat of fusion, it is also relative to the heat transferred and mass. Since

the mass of the ice of both trial is the same, the greater the heat transferred the greater the computed

latent heat of fusion. Thus, we can say that it is proportional to the heat transferred and inversely

proportional to the mass. Whilst, the specific heat is also proportional to the heat transferred but

inversely proportional to mass and the temperature change.

REFERENCES

Serway, R. A., & Jewett Jr., John W. (2014). University Physics. Philippines: Cengage Learning

Asia Pte Ltd.

0.2397

1.02E-01

0.2174

0.0932

0

0.1

0.2

0.3

Aluminium Metal Copper MetalSPEC

IFIC

HEA

T C

AP

AC

ITY

COMPARISON OF RELEVANT VALUE TO THE ACTUAL VALUE

Specific Heat Capacity of the Metals

Experimental Value ofSpecific Heat Capacity

Actual Value of SpecificHeat Capacity

80 9.65E+016.59E+01

0

50

100

150

Actual Value Trial 1 Trial 2

LATE

NT

HEA

T O

F FU

SIO

N

VALUE PER TRIAL

Latent Heat of Fusion (Ice)

PHOTOS

Photo 1: Measuring the temperature of the

calorimeter.

Photo 2: Measuring the mass of calorimeter.

Photo 3: Boiling the copper metal.

Figure 4: Set-up of the experiment