Final answer:
To raise the temperature of 25kg of water in a bathtub from 25°C to body temperature (37°C), you would need approximately 4.8 kg of boiling water, assuming no heat is transferred to the surrounding environment.
Step-by-step explanation:
To determine how much boiling water you would need to raise the bath to body temperature (about 37°C) from a starting temperature of 25°C for a bathtub containing 25kg of water, we can use the concept of heat transfer and specific heat capacity. The specific heat capacity of water is 4,184 Joules/kg°C, which means it takes 4,184 Joules to raise the temperature of 1 kg of water by 1°C. We are looking to raise the temperature by 12°C (from 25°C to 37°C).
Using the formula:
Q = mc∆T
Where:
Q = heat energy (in Joules)
m = mass (in kilograms)
c = specific heat capacity (J/kg°C)
∆T = change in temperature (in °C)
The heat energy required to raise the temperature of 25 kg of water from 25°C to 37°C can be calculated as follows:
Q = (25 kg) × (4,184 J/kg°C) × (37°C - 25°C)
Q = (25 kg) × (4,184 J/kg°C) × (12°C)
Q = 1,258,800 Joules
Since we know that boiling water is at 100°C, the temperature difference between boiling water and the desired bath temperature is 100°C - 37°C = 63°C. The amount of boiling water needed can be found by setting the heat transfer from the boiling water (Q) equal to the heat required to warm the bathwater to body temperature and solving for the mass (m) of boiling water needed:
Q = m × (4,184 J/kg°C) × (63°C)
1,258,800 J = m × (4,184 J/kg°C) × (63°C)
m = 1,258,800 J / ((4,184 J/kg°C) × (63°C))
m ≈ 4.8 kg
Thus, you would need approximately 4.8 kg of boiling water to raise the bath to body temperature.