How much boiling water would you need in order to raise the bath to body temperature (about 37\rm {}^\circ C)? Assume that no heat is transferred to the surrounding environment.
John, I did this a day or so ago.
To find out the amount of boiling water needed to raise the bath to body temperature, we can use the formula for heat transfer, which is given by:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
In this case, we want to find the mass of water (m), so we rearrange the formula to solve for m:
m = Q / (c * ΔT)
To calculate Q, we need to know the specific heat capacity of water. The specific heat capacity of water is approximately 4.186 Joules per gram per degree Celsius (J/g°C).
Now, let's calculate the value of Q. The initial temperature of the bath is not given, so let's assume it is room temperature (around 25°C). The desired final temperature is 37°C.
ΔT = (final temperature) - (initial temperature) = 37°C - 25°C = 12°C
Now, we can calculate Q using the formula:
Q = mcΔT
Let's assume the mass of the bathwater is 100 kilograms (kg):
Q = (100,000 grams) * (4.186 J/g°C) * (12°C) = 502,320 Joules (J)
So the amount of heat transfer required to raise the bathwater to body temperature is 502,320 Joules (J).
Now, let's calculate the mass of boiling water required using the formula:
m = Q / (c * ΔT)
m = (502,320 J) / (4.186 J/g°C * 100°C) = 1,200 grams
Therefore, you would need approximately 1,200 grams (or 1.2 kilograms) of boiling water to raise the bath to body temperature.