JAMB Physics 2021 Paper

Concept: When the substance falls, its gravitational potential energy is completely converted into heat energy, which raises its temperature.Explanation:The potential energy lost by the substance is given by $mgh$. This energy is entirely absorbed as heat, so $Q = mgh$. The heat needed to raise the temperature is $Q = mc\Delta\theta$. Equate the two expressions: $$mc\Delta\theta = mgh$$ Cancel the mass $m$ from both sides: $$c\Delta\theta = gh$$ Solve for the temperature rise: $$\Delta\theta = \frac{gh}{c}$$ Substitute $g = 10 \, \text{ms}^{-2}$, $h = 20 \, \text{m}$, and $c = 450 \, \text{Jkg}^{-1}\text{K}^{-1}$: $$\Delta\theta = \frac{10 \times 20}{450} = \frac{200}{450} = \frac{4}{9}$$ Therefore, the rise in temperature is $\frac{4}{9}\,{}^{\circ}\text{C}$.Answer: B. $\frac{4}{9}\,{}^{\circ}\text{C}$