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Physics

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Answers

2 parts
b

3150 J\text{3150 J}

c

450 J kg−1 K−1\text{450 J kg}^{-1} \text{ K}^{-1}

Step-by-step solution

4 steps

Here are the solutions to the questions based on the image:

Part a

Calculate the heat lost by the pendulum bob.

To find the heat lost by the pendulum bob, we first need to calculate the heat gained by the water, assuming no heat loss to the surroundings.

Part b

3150 J\text{3150 J}

Calculate the heat gained by the water.

  1. Identify the given values for water.

    Mass of water (mwm_w) = 150 g = 0.15 kg
    Specific heat capacity of water (cwc_w) = 4200 J kg−1^{-1} K−1^{-1}
    Initial temperature of water (θwi\theta_{wi}) = 25 °C
    Final temperature of water (θwf\theta_{wf}) = 30 °C
    Change in temperature of water (Δθw\Delta \theta_w) = θwf−θwi\theta_{wf} - \theta_{wi} = 30 °C - 25 °C = 5 °C

  2. Calculate the heat gained by the water.

    Qw=mwcwΔθwQ_w = m_w c_w \Delta \theta_w Qw=(0.15 kg)×(4200 J kg−1 K−1)×(5 K)Q_w = (0.15 \text{ kg}) \times (4200 \text{ J kg}^{-1} \text{ K}^{-1}) \times (5 \text{ K}) Qw=3150 JQ_w = 3150 \text{ J}

    The heat gained by the water is 3150 J\boxed{\text{3150 J}}.

    Now, we can answer part (a).
    Assuming that all the heat lost by the pendulum bob is gained by the water:

    Qlost,bob=Qgained,waterQ_{lost, bob} = Q_{gained, water} Qlost,bob=3150 JQ_{lost, bob} = 3150 \text{ J}

    The heat lost by the pendulum bob is 3150 J\boxed{\text{3150 J}}.

Part c

450 J kg−1 K−1\text{450 J kg}^{-1} \text{ K}^{-1}

Calculate the specific heat capacity of the material of the pendulum bob.

  1. Identify the given values for the pendulum bob and the heat lost.

    Mass of pendulum bob (mbm_b) = 100 g = 0.1 kg
    Initial temperature of pendulum bob (θbi\theta_{bi}) = 100 °C
    Final temperature of pendulum bob (θbf\theta_{bf}) = 30 °C
    Change in temperature of pendulum bob (Δθb\Delta \theta_b) = θbi−θbf\theta_{bi} - \theta_{bf} = 100 °C - 30 °C = 70 °C
    Heat lost by pendulum bob (QbQ_b) = 3150 J (from part a)

  2. Calculate the specific heat capacity of the pendulum bob (cbc_b).

    Qb=mbcbΔθbQ_b = m_b c_b \Delta \theta_b cb=QbmbΔθbc_b = \frac{Q_b}{m_b \Delta \theta_b} cb=3150 J(0.1 kg)×(70 K)c_b = \frac{3150 \text{ J}}{(0.1 \text{ kg}) \times (70 \text{ K})} cb=31507 J kg−1 K−1c_b = \frac{3150}{7} \text{ J kg}^{-1} \text{ K}^{-1} cb=450 J kg−1 K−1c_b = 450 \text{ J kg}^{-1} \text{ K}^{-1}

    The specific heat capacity of the material of the pendulum bob is 450 J kg−1 K−1\boxed{\text{450 J kg}^{-1} \text{ K}^{-1}}.

Part d

State two precautions taken to ensure accurate results.

  • Transfer the pendulum bob quickly from beaker A to beaker B to minimize heat loss to the surroundings during transfer.
  • Stir the water in beaker B continuously to ensure uniform heat distribution and an accurate final equilibrium temperature reading.

Part e

State two sources of error in the experiment.

  • Heat loss to the surroundings: Some heat may be lost from the hot pendulum bob or the water to the air and the beaker, which is not accounted for.
  • Incomplete heat transfer: The pendulum bob might not have reached exactly 100 °C in the boiling water, or not all its heat was transferred to the water in beaker B.
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