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

A fixed mass of water was used throughout the experiment for several reasons:

1. Consistency: Keeping the mass of water constant ensures that the results are reliable and can be compared directly for different current values.
2. Simplification of Variables: It minimizes the number of variables affecting the temperature change; since Δθ varies with both the amount of heat absorbed (which depends on mass) and the specific heat capacity, fixing the mass isolates the effect of the current.
3. Accuracy in Temperature Measurement: With a constant mass, any change in temperature can be attributed directly to the electrical energy supplied, allowing for a clearer correlation with Joule's law.

The graph plotted temperature change Δθ against the square of the current I² shows a linear relationship, indicating a direct proportionality, consistent with Joule's law which states that the heat produced by an electric current is proportional to the square of the current:

$Q = I^2 R t$

Where Q is the heat energy absorbed, I is the current, R is the resistance, and t is the time of flow. In this case:

• Straight Line Graph: A straight line through the origin indicates that as the current increases, the temperature change also increases proportionally, confirming that the heat generated is proportional to the square of the current.
• Constant Resistance: The slope of the graph can be interpreted as related to the resistance of the heating coil, reinforcing the direct relationship stated in Joule's law.

Firstly, we need to convert the mass of water from grams to kilograms: $m = 90 g = 0.090 kg$

The specific heat capacity of water is given as 4200 J kg⁻¹ K⁻¹. The energy absorbed by the water can be calculated using:

$Q = mcΔθ$

If we take a point from the graph, for instance, at I = 2 A where Δθ = 12 K, the energy absorbed would be: $Q = 0.090 imes 4200 imes 12$

Now calculate the resistance (R) using Joule's law: $P = I^2 R$ Where P = total power delivered. The power can also be calculated from Q: P = rac{Q}{t} Here, time t = 3 minutes = 180 seconds.

Thus,

1. Calculate Q
2. Find P
3. Rearranging gives: R = rac{P}{I^2} Using the values from the graph and calculated data, we can determine the resistance of the heating coil.