Question

Compare a coffee cup of boiling water and a bathtub full of room temperature water and answer the following questions;

Which has more thermal energy?
Which has a higher temperature?
Explain how the energy of the particles in each will help determine the answer.

Answer 1

To compare a coffee cup of boiling water and a bathtub full of room temperature water, let's analyze the questions one by one.

### 1. Which has more thermal energy?
**Answer:** The bathtub full of room temperature water has more thermal energy.

**Explanation:** Thermal energy is related to the mass of the substance as well as its temperature. While the boiling water (100°C) has a higher temperature than room temperature water (around 20-22°C), the total thermal energy is also dependent on the amount of substance present. A bathtub can hold significantly more water (for instance, 150 liters or more) than a single coffee cup (which might hold around 250-350 ml). Therefore, the larger mass of water in the bathtub results in a greater total thermal energy, despite the boiling water being at a higher temperature.

### 2. Which has a higher temperature?
**Answer:** The coffee cup of boiling water has a higher temperature.

**Explanation:** Temperature is a measure of the average kinetic energy of the particles in a substance. Since the boiling water is at 100°C, it has a higher temperature than the water in the bathtub, which is at room temperature (around 20-22°C).

### 3. Explain how the energy of the particles in each will help determine the answer.
**Answer:**

- **Temperature and Particle Energy:** The temperature reflects the average kinetic energy of the molecules in the water. In the boiling water, the molecules are moving rapidly due to the high temperature, indicating higher average kinetic energy. This is what gives boiling water its higher temperature.

- **Thermal Energy and Particle Count:** Thermal energy, on the other hand, accounts for both the temperature and the number of particles present. Even though the room temperature water has a lower average kinetic energy (lower temperature), the sheer quantity of water molecules in the bathtub contributes to a total thermal energy that is much greater than that of a smaller amount of boiling water.

In essence, temperature determines how fast the particles are moving on average, while thermal energy considers both how fast they are moving and how many particles there are. In this scenario, while the boiling water has a higher temperature due to high particle motion, the bathtub's greater mass results in higher overall thermal energy.