Question

Which of the following processes are spontaneous? (a) a ball rolling down a hill (b) a drop of ink dispersing in water (c) melting wax at \(10^{\circ} \mathrm{C}\)

Short answer

A ball rolling down a hill is a spontaneous process, as it occurs naturally due to the force of gravity pulling the ball towards the center of the Earth. A drop of ink dispersing in water is also a spontaneous process, as it is driven by the random motion of ink and water molecules, causing the ink to spread out and mix with the water. However, melting wax at \(10^{\circ} \mathrm{C}\) is a non-spontaneous process because wax typically has a melting point above room temperature, and external input, such as heating the wax, is required for the melting process to occur.

Step-by-step solution

(a) A Ball Rolling Down a Hill

A ball rolling down a hill is a spontaneous process. It occurs naturally due to the force of gravity pulling the ball towards the center of the Earth. The potential energy of the ball at the top of the hill is converted into kinetic energy as it rolls downhill, without any external input or assistance needed.

(b) A Drop of Ink Dispersing in Water

A drop of ink dispersing in water is a spontaneous process. This process is driven by the random motion of ink and water molecules, causing the ink to spread out and mix with the water. This dispersion of ink molecules happens naturally, without any external input or assistance required.

(c) Melting Wax at \(10^{\circ} \mathrm{C}\)

Melting wax at \(10^{\circ} \mathrm{C}\) is a non-spontaneous process. Wax has a melting point above room temperature, typically around \(45^{\circ} \mathrm{C}\) to \(65^{\circ} \mathrm{C}\). This means that at room temperature or below (e.g., \(10^{\circ} \mathrm{C}\)), wax remains in its solid state and does not melt spontaneously. External input, such as heating the wax, is required for the melting process to occur.