Lab 2 - Specific Heat of Aluminum PDF

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THE SPECEFIC HEAT OF ALUMINUM
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THE SPECEFIC HEAT OF ALUMINUM ASHLEY BROWN PARTNER: JOHNATHON PHYSICS LAB II SECTION 02B TA – LJUBICA AND MEHDI

UNIVERSITY OF MASSACHUSETTS BOSTON JULY 31ST, 2017

Purpose The purpose of this experiment is to review the physical concepts and relationships associated with the flow of heat in and out of materials by determining the specific heat of aluminum in the temperature range between boiling water and room temperature water. By doing so, we will come to a deeper understanding of the principle of conservation of energy as it applies to thermal energy. Data Table Mass Cube N T (g) 5 (C) 44.3 mΑl 23.0 44.3 (g) 23.0 44.4 44.3000 23.3 44.2 Sm 23.0 44.3 (g) 23.0 0.0707 SmAl (g) 0.0316

N

Mc 5 (g)

T (C) Mc+w 23.0600 (g) ST (C) Mw 0.1342 (g) ST (C) Smw 0.0600

Ti,w ΔTw CAl,exp CAl,acc (°C) (°C) (cal/(g*°C)) (cal/(g*°C)) 4.51 20.90 8.6000 0.1910 0.2150 Ti, Al SΔTw S`Cal,exp Cw (°C) (°C) (cal/(g*°C)) 0.9982 74.00 100.00 0.1897 0.0042 Tf ΔTAl %dif (°C) (°C) 11.1576 69.49 29.50 70.5000 SΔTAl 0.1000 (°C) 0.1342

Table 1 – Contains measurements obtained leading to the specific heat of Aluminum. This table includes 1D Stats performed on the Mass of the Cube, and the Temperature of the Room. Calculations and Analyses The mass of water used in this experiment was calculated

Values obtained through 1D Stats: mΑl, Sm, SmAl, T, ST, ST

at 69.49 g. The change in water temperature was calculated at 8.60 C. The calculated experimental value for the specific heat of Aluminum was calculated at 0.1910 cal/g*C. When compared to the accepted value of the specific heat of Aluminum, the percent different was 11.16%. Since this percent is not close to 0, there is an implication that there were errors made while obtaining measurements.

mw = mc+w – mc 69.49 g = 74.00 g – 4.51 g Smw = (Sm)2 + (Sm)2 0.1000 = (0.0707)2 + (0.0707)2 ΔTw = Tf – Ti,w 8.60 C = 29.50 C – 20.90 C SΔTw = (ST)2 + (ST)2 0.1897 C = (0.1342 C)2 + (0.1342 C)2 SΔTAl = ST 0.1342 C = 0.1342 C

CAl,exp = (mwcwΔTw)  (mΑlΔTAl ) 0.1910 cal/g*C = (69.49g  0.9982  8.60C)  (44.30g  70.50 C) SCAl,exp = CAl,exp  (Smw / mw)2 + (SΔTw / ΔTw)2 + (SmΑl / mΑl)2 + (SΔTAl / ΔTAl)2 0.0042 cal/g*C = 0.1910 cal/g*C  (0.1000C/0.1897C)2 + (0.1897C/8.60C)2 + (0.0316g/44.30g)2 + (0.1342C/70.50C)2 %diff = | (CAl,exp - CAl,acc ) / ( CAl,exp ) |  100 11.16% = |(0.1910 cal/g*C – 0.2150 cal/g*C) / (0.2150 cal/g*C) |  100

Questions 1.) If we were to have not ignored the mass and specific heat of the thermometer, the measurement of heat capacity of Aluminum might have been lower. If we were to have considered the specific heat and mass, then by the time the thermometer reached equilibrium with the water and the Aluminum cube, the water would have already cooled somewhat by energy loss to its surroundings. The specific heat of the Aluminum depends on the specific heat of the water. 2.) If the thermometer were not properly calibrated in this experiment, we would have resulted in systematic errors. It would be systematic because all of the data is off in the same direction, making it hard to detect. This makes it hard to spot the error by analyzing it statistically. 3.) If 200.00 grams of tap water were used in this experiment the temperature of the water would have to reach room temperature, and the mass of the cube would have to increase. We would have to increase the mass if the cube because we would need to add for heat to obtain the same change in temperature. 4.) In the equations below, Tf was changed in two different ways to see which would affect the specific heat of Aluminum more. When the Tf was changed (Ti,Al – Tf) the specific heat of Aluminum decreased by a small amount, but when Tf was changed (Tf – Ti,w), the specific heat of Aluminum was increased drastically. This reveals that when incorporating the thermometer into the experiment, more error is associated with the experimental value of the specific heat of Aluminum. ΔTAl = (Ti,Al – Tf) ΔTAl = (100.00C - 0.1342 C) = 99.8658 C CAl,exp = (mwcwΔTw)  (mΑlΔTAl ) CAl,exp = (69.49g  0.9982  8.60C)  (44.30g  99.8658 C) = .1348 cal/g*C ΔTAl = (Tf – Ti,w) ΔTAl = (0.1342C – 20.90C) = 20.7658 C CAl,exp = (mwcwΔTw)  (mΑlΔTAl ) CAl,exp = (69.49g  0.9982  8.60C)  (44.30g  20.7658C) = 0.6468 cal/g*C

Discussion This experiment revealed that the specific heat of substances varies with the temperature. In this experiment, the specific heat of Aluminum was dependent on the

temperature and mass of that water when calculating the specific heat. The experimental calculated value of the Aluminum cube was 0.1910 cal/g*C. The accepted specific heat value of Aluminum is 0.2150 cal/g*C. The experimental value obtained was lower than the accepted, which gave us a percent difference of 11.16%. This high percent error could be due to potential errors that took place in the lab. In this experiment, the apparatus used to measure the boiling water at 100C was a digital thermometer. When the water was at its boiling point, the digital thermometer was reading 101.35C. Even though this measurement is wrong, because water boils at 100C, this was an indication that the digital thermometer was not properly calibrated. Secondly, we may not have had the Aluminum cube submerged in the boiling water long enough for the cube to reach 100C. If this were the case, then the equilibrium reached between the cube and the water would have been inaccurate because we were using a Tf value of 100C. Lastly, the mass of the water could have been off by  0.5 g. The mass of the water could be off because when measuring the mass of the water, there were water droplets on the side of the cup and on the double pan balance that were measured, but not actually accounted for when the cube was submerged into the water. If we were to take all three of these errors and consider that they all were true when performing this experiment, they could account for the percent error being so high. When using multiple apparatuses in an experiment, there is more chance for error because with each apparatus there is a chance for improper calibration. Conclusion The mass of water used in this experiment was calculated at 69.49 g. The change in water temperature was calculated at 8.60 C. The calculated experimental value for the specific heat of Aluminum was calculated at 0.1910 cal/g*C. When compared to the accepted value of the specific heat of Aluminum, the percent different was 11.16%. There were potential systematic and random errors when performing this experiment....