Design an experiment to determine the specific heat capacity of an unknown metal.

Here's a breakdown of the experiment and tasks:

Phase 2: Experimental Design and Execution

Task 2.1: Design your experiment by:

• Listing all materials and equipment:

  • Calorimeter (e.g., polystyrene cup with lid)
  • Thermometer (digital or mercury-in-glass)
  • Stirrer
  • Unknown metal sample (e.g., metal block or pellets)
  • Water
  • Beaker (for heating water and metal)
  • Thread (to suspend metal)
  • Heat source (e.g., Bunsen burner, hot plate)
  • Electronic balance (for measuring mass)
  • Clamp stand and clamp (to hold thermometer or metal)

• Drawing a labelled diagram of the setup:

  • Description: The setup involves two main parts. First, a beaker on a heat source containing water, with the metal sample suspended by a thread in the boiling water, and a thermometer to confirm the water's temperature. Second, a calorimeter (e.g., a polystyrene cup with a lid) containing a known mass of water, a stirrer, and a thermometer. The hot metal is quickly transferred from the boiling water to the calorimeter.

• Identifying sources of error and ways to minimize them:

  • Sources of Error:
    • Heat loss to surroundings: The calorimeter is not perfectly insulated, leading to heat exchange with the environment.
    • Incomplete heat transfer: The metal might not reach the exact boiling point of water, or it might lose heat during transfer to the calorimeter.
    • Temperature measurement inaccuracies: Errors in reading the thermometer or thermometer calibration issues.
    • Mass measurement inaccuracies: Errors in using the balance.
    • Specific heat capacity of calorimeter: The assumed value for $c_c$ might not be perfectly accurate.
    • Inadequate stirring: Leads to non-uniform temperature distribution in the water.
  • Ways to Minimize Errors:
    • Heat loss: Use a well-insulated calorimeter (e.g., double-walled polystyrene cup with a lid). Minimize the time taken to transfer the hot metal.
    • Incomplete heat transfer: Ensure the metal is immersed in boiling water for a sufficient duration (e.g., 10-15 minutes) to reach thermal equilibrium. Transfer the metal quickly.
    • Temperature measurement: Use a precise thermometer and read at eye level. Stir continuously for uniform temperature.
    • Mass measurement: Use a precise digital balance and zero it correctly.
    • Calorimeter specific heat capacity: Use a calorimeter made of a known material or determine its specific heat capacity experimentally.
    • Stirring: Stir the water gently but continuously.

Task 2.2: Conduct the experiment:

• Record all measurements in a data table:
  • A data table should include: mass of calorimeter ($m_c$), mass of water ($m_w$), initial temperature of water and calorimeter ($\theta_1$), mass of metal ($m_s$), initial temperature of metal ($\theta_2$, typically boiling point of water), and final equilibrium temperature ($\theta_f$).
• Conduct at least two trials for reliability: Repeat the entire experiment at least twice to check for consistency and calculate an average.
• Ensure accurate measurements with proper units: All measurements should be taken carefully and recorded with their correct SI units (e.g., kg for mass, $^\circ C$ or K for temperature).

Phase 3: Data Analysis and Calculation

Task 3.1: Calculate the specific heat capacity using the formula:

The formula provided is:

$$c_s = \frac{m_w c_w (\theta_f - \theta_1) + m_c c_c (\theta_f - \theta_1)}{m_s (\theta_2 - \theta_f)}$$

Where:

• $c_s$: specific heat capacity of metal (to be calculated)
• $m_w$: mass of water (in kg)
• $c_w$: specific heat capacity of water ($4186 \text{ J kg}^{-1} \text{ K}^{-1}$)
• $m_c$: mass of calorimeter (in kg)
• $c_c$: specific heat capacity of calorimeter (in $\text{J kg}^{-1} \text{ K}^{-1}$, depends on material, e.g., copper is $\approx 385 \text{ J kg}^{-1} \text{ K}^{-1}$, polystyrene is $\approx 1300 \text{ J kg}^{-1} \text{ K}^{-1}$)
• $\theta_f$: final equilibrium temperature (in $^\circ C$ or K)
• $\theta_1$: initial temperature of water and calorimeter (in $^\circ C$ or K)
• $m_s$: mass of metal (in kg)
• $\theta_2$: initial temperature of metal (in $^\circ C$ or K, typically $100^\circ C$)

To calculate $c_s$, substitute all measured and known values into the formula and solve.

Task 3.2:

• Calculate average specific heat capacity from your 2 trials:
  • If you obtain $c_{s, \text{trial 1}}$ and $c_{s, \text{trial 2}}$ from two trials, the average specific heat capacity is: $$c_{s, \text{average}} = \frac{c_{s, \text{trial 1}} + c_{s, \text{trial 2}}}{2}$$
• Compare with known specific heat capacity value of the metal:
  • Once the metal is identified, find its accepted specific heat capacity value from a reliable source. Compare your calculated average value to this accepted value.
• Calculate percentage error:
  • Percentage Error $= \frac{| \text{Experimental Value} - \text{Accepted Value} |}{\text{Accepted Value}} \times 100\%$

Phase 4: Analysis and Interpretation

Task 4.1: Analyze results:

• Was the calculated value close to the known value? Explain.
  • Based on your percentage error, determine if the experimental value is acceptably close to the known value. A small percentage error (e.g., less