The increase in water temperature resulting from pouring boiling water into a swimming pool would depend on several factors, such as the size and temperature of the pool, as well as the initial temperature of the water. However, we can make some estimations based on general assumptions.
Assuming the pool is large enough that the 2 gallons of boiling water can disperse evenly throughout the entire volume of the pool, we can calculate the potential temperature increase. Keep in mind that this is a simplified approximation and may not reflect real-world conditions accurately.
First, we need to convert gallons to liters for consistent units. One gallon is approximately equal to 3.785 liters. Therefore, 2 gallons would be approximately 7.57 liters.
Next, we need to consider the specific heat capacity of water, which is the amount of energy required to raise the temperature of water by a certain degree. For water, the specific heat capacity is approximately 4.18 Joules per gram per degree Celsius (J/g°C).
Assuming the initial temperature of the pool water is around 20°C (68°F), and the boiling water is around 100°C (212°F), we can calculate the energy released by the boiling water:
Energy = mass of water * specific heat capacity * temperature difference
The mass of 7.57 liters (7,570 grams) of water is 7,570 grams.
Energy = 7,570 g * 4.18 J/g°C * (100°C - 20°C) = 2,213,164 J
Now, to determine the increase in temperature of the entire pool, we need to know the total volume of the pool and its mass. Let's assume we have a small pool with a volume of 10,000 liters (10,000 kg) for simplicity.
To calculate the resulting temperature increase, we divide the energy released by the total mass of the pool water:
Temperature increase = Energy / (total mass * specific heat capacity)
Temperature increase = 2,213,164 J / (10,000 kg * 4.18 J/g°C) = 52.96°C
Therefore, pouring 2 gallons (7.57 liters) of boiling water into a 10,000-liter pool with an initial temperature of 20°C could potentially increase the water temperature by approximately 52.96°C. However, please note that this is a simplified estimation, and many real-world factors can affect the final temperature increase, such as pool size, insulation, and heat dissipation.