Question

Compare the heat energy in a teaspoon of boiling water and a swimming pool full of room temperature water

Answer 1

To compare the heat energy in a teaspoon of boiling water to that in a swimming pool full of room temperature water, we need to look at both the quantity of water and its temperature.

1. **Heat Energy Calculation**:
- The amount of heat energy in a substance can be calculated using the formula:
\[
Q = mc\Delta T
\]
where \( Q \) is the heat energy, \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (approximately \( 4.18 \, \text{J/g°C} \)), and \( \Delta T \) is the change in temperature.

2. **Teaspoon of Boiling Water**:
- A teaspoon of water is approximately 5 mL, which has a mass of about 5 grams (since 1 mL of water has a mass of roughly 1 gram).
- If the boiling point of water is 100°C and the room temperature is about 20°C, the change in temperature (\( \Delta T \)) for boiling water (if we were to cool it down to room temperature) would be 80°C.
- Thus:
\[
Q_{\text{teaspoon}} = m \cdot c \cdot \Delta T = 5 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot 80 \, \text{°C} \approx 1672 \, \text{J}
\]

3. **Swimming Pool Full of Room Temperature Water**:
- A standard swimming pool holds about 50,000 liters of water, which is 50,000 kg (since 1 liter of water has a mass of 1 kg).
- If the water in the pool is at room temperature (let’s say 20°C), and we will assume we want to heat this water to boiling (or for comparison, just looking at the energy at room temperature):
- The amount of heat energy in this case is still \( 0 \) for room temperature since we are not considering any temperature change. However, if we want to calculate the total heat energy for reference:
\[
Q_{\text{pool}} = m \cdot c \cdot T = 50,000 \, \text{kg} \cdot 4.18 \, \text{J/kg°C} \cdot 20 \, \text{°C} \approx 4,180,000 \, \text{J}
\]

4. **Comparison**:
- The heat energy in a teaspoon of boiling water (1672 J when cooled to room temperature) is minuscule compared to the heat energy present in a swimming pool full of room temperature water (about 4,180,000 J).
- Therefore, while the boiling water has significantly more energy per unit (due to its higher temperature), the sheer volume of the swimming pool gives it much more total heat energy.

In conclusion, the swimming pool contains vastly more heat energy overall compared to a single teaspoon of boiling water, primarily due to the larger mass of water.