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In an experiment to verify Joule’s law a student passed a current through a heating coil in a calorimeter containing a fixed mass of water and measured the rise in temperature Δθ for a series of different values of the current I - Leaving Cert Physics - Question 4 - 2006
Question 4
In an experiment to verify Joule’s law a student passed a current through a heating coil in a calorimeter containing a fixed mass of water and measured the rise in t... show full transcript
Worked Solution & Example Answer:In an experiment to verify Joule’s law a student passed a current through a heating coil in a calorimeter containing a fixed mass of water and measured the rise in temperature Δθ for a series of different values of the current I - Leaving Cert Physics - Question 4 - 2006
Step 1
Describe, with the aid of a labelled diagram, how the student arranged the apparatus.
Answer
The apparatus consists of a power supply, a coil (heating element), an ammeter to measure current, and a thermometer to record the temperature of the water.
- Power Supply: Connect to provide a variable current through the circuit.
- Coil: Inserted in the calorimeter, this heating element generates heat when current flows through it.
- Ammeter: Connected in series to measure the current supplied.
- Calorimeter: Contains a fixed mass of water to ensure accurate measurements of temperature changes.
- Thermometer: Placed in the water to measure the temperature rise accurately.
A labelled diagram will illustrate these components and their connections.
Step 2
Why was a fixed mass of water used throughout the experiment?
Answer
A fixed mass of water was used to ensure that the temperature increase due to the current passing through the coil can be accurately calculated. By keeping the mass constant, variations in temperature rise can be directly related to the electrical energy supplied without confounding factors affecting the results.
Step 3
The student drew a graph, as shown. Explain how this graph verifies Joule’s law.
Answer
The graph shows the relationship between the rise in temperature, Δθ (in K), and the square of the current, I² (in A²). According to Joule's law, the heat produced is proportional to the square of the current, which can be expressed as: This implies that if the graph depicts a straight line, then a linear relationship exists between Δθ and I², affirming that the energy supplied is consistent with Joule's law.
Step 4
Given that the mass of water in the calorimeter was 90 g in each case, and assuming that all of the electrical energy supplied was absorbed by the water, use the graph to determine the resistance of the heating coil.
Answer
- Start by noting the mass of the water, which is 90 g or 0.090 kg.
- Apply the formula for heat: where Q is heat energy, m is mass, c is specific heat capacity (4200 J kg⁻¹ K⁻¹), and Δθ is the temperature change from the graph.
- From the graph, use the appropriate slope for I² versus Δθ. Use two points to determine Δθ and extract the slope.
- Finally, use: where P can be deduced from the energy supplied, setting up the relationship between total energy, resistance, and the squared current.