To compare the heat energy in a teaspoon of boiling water and a swimming pool full of room temperature water, we need to consider both the specific heat capacity of water and the masses involved.
-
Teaspoon of Boiling Water:
- A teaspoon holds about 4.9 milliliters (mL) or approximately 4.9 grams (since the density of water is about 1 g/mL).
- Boiling water is at 100°C.
-
Swimming Pool of Room Temperature Water:
- A standard swimming pool is typically around 50,000 liters or more, which is about 50,000,000 grams.
- Room temperature water is usually around 20°C.
Calculating Heat Energy
The heat energy (Q) in a mass of water can be calculated using the formula:
\[ Q = mc\Delta T \]
Where:
- \( m \) = mass of the water (in grams)
- \( c \) = specific heat capacity of water (approximately \( 4.18 , \text{J/g°C} \))
- \( \Delta T \) = change in temperature (in °C)
1. Heat Energy in the Teaspoon of Boiling Water
Assuming the boiling water is cooling down to room temperature (from 100°C to 20°C):
- Mass \( m = 4.9 , \text{g} \)
- \( \Delta T = 100 - 20 = 80 , \text{°C} \)
Calculating \( Q \):
\[ Q_{teaspoon} = 4.9 \times 4.18 \times 80 \] \[ Q_{teaspoon} ≈ 1,636.64 , \text{J} \]
2. Heat Energy in the Swimming Pool
Assuming the pool is at room temperature:
- Mass \( m = 50,000,000 , \text{g} \)
- \( \Delta T = 20 - 20 = 0 , \text{°C} \) (no change in temperature)
Calculating \( Q \):
Since the temperature doesn't change, the heat energy to maintain this temperature doesn’t change, but we can calculate the total energy:
As the water is just at room temperature, we focus on the energy present, which, while not cooling down, can be thought of as the energy stored at that temperature.
\[ Q_{pool} = 50,000,000 \times 4.18 \times 0 = 0 , \text{J} \]
However, to compare the absolute energy stored at 20°C, we can just note that it's already at equilibrium, and thus doesn't change.
Comparison
- The boiling water has approximately 1,636.64 J of heat energy when cooling to room temperature.
- The swimming pool, while not undergoing a temperature change, contains a vastly greater volume of water, and any interaction with a heating source would involve calculations of the total thermal energy present.
Thus, the significant factor is:
- While a teaspoon of boiling water contains the heat energy of about 1,636.64 J, the swimming pool, albeit at equal room temperature, contains a tremendous amount of thermal energy due to its mass (around 50,000,000 grams).
So, the pool has much more total heat energy, even if it's at a cooler temperature overall. In simpler terms, the total energy content of the swimming pool is far greater than that of a single teaspoon of boiling water despite the differences in temperature.