In a Joule experiment a 12 kg weight falls 1.5 m and turns a paddle wheel in an insulated tank of…

Step 1. Work. $W = 12\ \text{kg} \times 9.8\ \text{m/s}^2 \times 1.5\ \text{m} \times 25 = 4410\ \text{J}$, done on the water.

Step 2. First law. $Q = 0$, so $\Delta U = 4410\ \text{J}$.

Step 3. Rise. $\Delta T = \dfrac{4410\ \text{J}}{4.0\ \text{kg} \times 4186\ \text{J kg}^{-1}\text{K}^{-1}} = 0.263\ \text{K}$.