Notes on Measuring Specific Heat of Metals

Experiment Overview

  • Experiment Number: 5

  • Topic: Measuring the specific heat of various metals

  • Objective: Determine the specific heat of known and unknown metal samples to identify unknown materials.

Experiment Setup

  • Equipment Used:

    • Beaker for heating the metal samples

    • Calorimeter (made of Styrofoam cups)

    • Thermometer

    • Water bath heated to boiling (100 degrees Celsius)

Metal Samples

  • First Sample: Copper (standard)

  • Heating Process: Copper will be heated in boiling water to 100 degrees Celsius before transferring it to the calorimeter.

  • Second Sample: Unknown metal (identified during the experiment)

Procedure

  1. Heating Copper Sample:

    • Heat a copper sample in a boiling water bath (100 degrees Celsius).

    • Record the temperature of the water in the calorimeter before adding the hot copper.

  2. Setting Up Calorimeter:

    • Prepare the calorimeter with about 100 ml of water.

    • Measure and record the initial temperature of the water.

    • Add the heated copper to the water and swirl for 1-2 minutes.

    • Measure the final temperature of the water after thermal equilibrium is reached.

  3. Experimental Trials:

    • Conduct two trials using the copper and two trials with the unknown metal, noting the temperature differences each time.

Specific Heat Equation

  • Definition: Specific heat is the amount of energy required to raise the temperature of one gram of a substance by one degree Celsius.

  • Formula: Q = m imes s imes riangle T where:

    • Q = amount of heat energy gained or lost (Joules)

    • m = mass of the substance (grams)

    • s = specific heat capacity (J/g°C)

    • riangle T = change in temperature (°C)

Key Concepts

  • Specific Heat of Common Materials:

    • Water: 1 cal/g°C (or 4.18 J/g°C)

    • Sand: ~1/5 of water’s specific heat

    • Air: ~1/4 of water’s specific heat

    • Metals (e.g., Gold): Extremely low specific heat, allowing it to heat up rapidly.

  • Insulation in Calorimeters:

    • The calorimeter must be well-insulated to ensure no heat escapes or enters from outside.

    • Using two Styrofoam cups enhances insulation.

Heat Exchange

  • The heat lost by the metal must equal the heat gained by the water:
    Q{metal} = Q{water}

  • Rearranging the formulas:
    m{water} imes s{water} imes (T{final} - T{initial, water}) = m{metal} imes s{metal} imes (T{initial, metal} - T{final})

  • Use this relationship to derive the specific heat of the unknown metal.

Experimental Data Example

  • Initial Water Temperature: 19.8 °C

  • Final Water Temperature after Heating: 23.3 °C

  • Mass of Water (m): Measured each trial

  • Calculate

    • Q{water} = m{water} imes s{water} imes (T{final} - T_{initial})

    • With values:
      Q_{water} = 100 g imes 4.18 ext{ J/g°C} imes (23.3 °C - 19.8 °C)

    • Result: 1486 J

Calculation of Specific Heat of Unknown Metal

  • Mass of Unknown Metal: e.g., 88.24 g

  • Change in Temperature (from 100 °C to final temperature): e.g., 76.7 °C

  • Substitute in the rearranged equation to solve for specific heat of unknown metal:
    s = rac{Q{water}}{m{metal} imes (T{initial} - T{final})}

Identifying Unknown Metal

  • Compare calculated specific heat values with a table of known specific heats for metals to identify the unknown.

  • If values are inconclusive, consider using density (calculated from previous density lab experiments) as additional identification.

Conclusion Tasks

  1. Calculate specific heat for copper in both trial experiments and compare with known values.

  2. Calculate specific heat for the unknown metal and compare with the known values to identify it.

  3. Answer all end-of-lab questions for submission preparing for analysis of thermal properties in metals.