In an experiment to verify Joule's law, a fixed mass of water was heated in an insulated cup, θ, the highest temperature reached, was recorded for different values of current, I - Leaving Cert Physics - Question 4 - 2014

To verify Joule’s law, plot a graph with the current squared ($I^2$) on the x-axis and the temperature change ($heta - 20.0$ °C) on the y-axis.

• Calculation of $I^2$ values:

  • For 1.0 A: $I^2 = 1.0^2 = 1$
  • For 1.5 A: $I^2 = 1.5^2 = 2.25$
  • For 2.0 A: $I^2 = 2.0^2 = 4$
  • For 2.5 A: $I^2 = 2.5^2 = 6.25$
  • For 3.0 A: $I^2 = 3.0^2 = 9$
  • For 3.5 A: $I^2 = 3.5^2 = 12.25$

• Axes labelled: Label the x-axis as "$I^2 / A^2$" and the y-axis as "$\Delta T / K$" where $\Delta T$ is the temperature change.

• Points plotted: Plot the calculated points based on the recorded data, ensuring accuracy.

• Straight line through origin: A straight line should fit well through the origin indicating that $P$ is proportional to $I^2$; this verifies Joule's law as it shows the relationship between heat produced and the square of the current.

From the graph, for $I = 1.6$ A, calculate $I^2 = 1.6^2 = 2.56$.
Using the graph, estimate the temperature change $\Delta T$ corresponding to $I^2 = 2.56$. Assuming from the graph that $\Delta T = 5.3$ °C, the final temperature will be: $T_{final} = 20.0 °C + \Delta T = 20.0 °C + 5.3 °C = 25.3 °C.$ Thus, the highest temperature reached is approximately 25.3 °C.

A fixed mass of water is essential in this experiment because it ensures that the variables are controlled. By maintaining a constant mass of water, we minimize variations in specific heat capacity, allowing for accurate verification of Joule's law. Different masses would introduce more variables affecting the heat output and temperature change, complicating the relationship being studied.