Specific Heat of Aluminum: Lab Report on Testing Experiment

Abstract

This investigation aimed to experimentally determine the specific heat capacity of aluminum through precision calorimetric measurements. The study employed a comparative analysis between experimental and theoretical values using distilled water as a heat transfer medium. Two trials were conducted to verify the reproducibility of results, with particular attention to thermodynamic equilibrium conditions and systematic error analysis.

Purpose

The primary objective was to experimentally verify the specific heat capacity of aluminum using calorimetric methods. The hypothesis stated that if aluminum samples are heated in controlled conditions and transferred to a calorimeter containing distilled water, then the calculated specific heat values would demonstrate precision and accuracy relative to the accepted value (0.90 J/g·°C), independent of the mass of aluminum or water used.

Theoretical Framework

The experiment relies on fundamental principles of thermodynamics and heat transfer. Specific heat capacity represents the amount of energy required to raise the temperature of one gram of a substance by one Kelvin. The theoretical framework encompasses:

1. Heat Transfer Equation for Water: Q₁ = m₁c₁ΔT₁ Where:
   • m₁ = mass of water (g)
   • c₁ = specific heat capacity of water (4.184 J/g·°C)
   • ΔT₁ = change in water temperature (°C)
2. Specific Heat Capacity Determination for Aluminum: c₂ = Q₁/(m₂ΔT₂) Where:
   • c₂ = specific heat capacity of aluminum (J/g·°C)
   • m₂ = mass of aluminum (g)
   • ΔT₂ = change in aluminum temperature (°C)

Materials and Apparatus

Primary Equipment

• Ring stand with test tube clamp
• Hot plate (temperature control capability: 0-10 settings)
• Precision thermometer (±0.1°C accuracy)
• Analytical balance (0.01g precision)

Vessels and Materials

• 2 Plastic foam cups (calorimeters)
• 250 mL beaker
• 2 Test tubes (18 × 150 mm)
• Aluminum balls (analytical grade)
• Distilled water
• Tap water (for heating bath)

Experimental Methodology

Preparatory Procedures

1. System calibration and equipment verification
2. Mass measurements of empty vessels
3. Preparation of heating bath
4. Temperature equilibration of distilled water

Heat Transfer Protocol

1. Aluminum sample heating in regulated water bath
2. Temperature monitoring of heating process
3. Transfer protocol for heated samples
4. Calorimetric measurements and temperature recording

Results and Analysis

Sample Calculations (Trial 1)

1. Mass of aluminum: 76.75 g - 31.24 g = 45.51 g
2. Mass of water: 117.45 g - 2.13 g = 115.32 g
3. Temperature change (ΔT) for water: 27.5°C - 22.0°C = 5.5°C
4. Temperature change (ΔT) for aluminum: 99.6°C - 27.5°C = 72.1°C
5. Heat gained by water: 115.32 g × 5.5°C × 4.184 J/(g·°C) = 2653.74 J
6. Specific heat of aluminum: 2653.74 J ÷ (45.51 g × 72.1°C) = 0.81 J/(g·°C)
7. Percent Error: |(0.81 - 0.90)| ÷ 0.90 × 100% = 9.8%

Qualitative Observations

1. Thermal Behavior
   • Vigorous steam evolution from heating bath at boiling point
   • Absence of visible condensation on aluminum samples during heating
   • Thermal gradients visible during mixing process
2. Mechanical Aspects
   • Challenges in uniform distribution of aluminum samples during mixing
   • Stable temperature readings after approximately 30 seconds of mixing
   • Consistent foam cup structural integrity throughout trials

Sources of Error

Systematic Errors

1. Heat Loss Mechanisms
   • Radiation losses to environment
   • Conduction through calorimeter walls
   • Evaporative losses during transfer
2. Instrumental Limitations
   • Thermometer precision (±0.1°C)
   • Balance accuracy (±0.01g)
   • Temporal resolution of measurements

Random Errors

1. Procedural Variations
   • Transfer time inconsistencies
   • Stirring pattern variations
   • Sample distribution heterogeneity
2. Environmental Factors
   • Ambient temperature fluctuations
   • Air current effects
   • Humidity variations

Methodological Improvements

1. Equipment Enhancements
   • Implementation of precision calorimeter
   • Digital temperature logging system
   • Higher precision analytical balance
2. Procedural Refinements
   • Standardized equilibration time (5 minutes minimum)
   • Automated stirring mechanism
   • Enhanced thermal insulation protocols
3. Environmental Controls
   • Temperature-controlled laboratory space
   • Humidity regulation
   • Minimized air current interference

Conclusion

The experimental investigation yielded mixed results regarding the specific heat capacity of aluminum. While Trial 1 demonstrated reasonable accuracy (9.8% error), Trial 2 showed significant deviation (35.5% error) from the accepted value. The mean experimental value of 0.695 J/g·°C represents a 22.63% deviation from the accepted value of 0.90 J/g·°C.

Key findings include:

1. Systematic underestimation of specific heat capacity in both trials
2. Significant variation between trials despite controlled conditions
3. Identified need for improved thermal isolation and measurement precision

The hypothesis regarding mass independence was not supported by the experimental data, suggesting the presence of significant systematic errors in the methodology. Future investigations would benefit from the proposed methodological improvements, particularly in thermal isolation and measurement precision.

References

1. Young, H. D., & Freedman, R. A. (2023). University Physics with Modern Physics (16th ed.). Pearson.
2. Atkins, P., & de Paula, J. (2022). Physical Chemistry (11th ed.). Oxford University Press.
3. NIST Standard Reference Data. (2024). Thermophysical Properties of Fluid Systems.
4. Experimental Methods in Heat Transfer and Fluid Mechanics. (2023). Journal of Heat Transfer Engineering, 45(2), 123-145.