How many gallons of water at 70 deg. F is required to cool a gallon of water at 212 deg f?

Cool 212 water to what. zero? 10? 99. 211? Pick a number and you'll be right.

Sorry,

Cool it to 100 deg F

To calculate the number of gallons of water at 70°F required to cool a gallon of water at 212°F, we need to apply the principle of heat transfer. The heat exchange equation can be used to find the equilibrium temperature between the hot and cold water:

m1 * C1 * (T1 - Teq) = m2 * C2 * (Teq - T2)

Where:
m1 = mass (or volume) of the hot water
C1 = specific heat capacity of water
T1 = initial temperature of the hot water
Teq = equilibrium temperature
m2 = mass (or volume) of the cold water
C2 = specific heat capacity of water
T2 = initial temperature of the cold water

In this case, we have a gallon of water at 212°F (T1) and we want to find the volume of water at 70°F (m2) required to cool it down. The specific heat capacity of water (C1 and C2) is assumed to be 1 BTU/lb°F.

Let's solve the equation step by step:

1. Convert the temperatures to Fahrenheit (if necessary):

T1 = 212°F
T2 = 70°F

2. Calculate the mass of the hot water (m1):
Since we have a gallon of water, we can assume the mass to be the same (mass = volume).

m1 = 1 gallon

3. Calculate the mass of the cold water (m2):
Since we want to find the mass of water needed to cool the hot water, we'll designate this as 'm2' and solve for it.

4. Plug the values into the equation and solve for the unknown (m2):

1 gallon * 1 BTU/lb°F * (212°F - Teq) = m2 * 1 BTU/lb°F * (Teq - 70°F)

Simplifying the equation:

212°F - Teq = m2 * (Teq - 70°F)

Combine like terms:

212°F - Teq = m2 * Teq - 70m2°F

Bring all the 'm2' terms to one side:

Teq + 70m2°F = Teq - 212°F

70m2°F = -212°F

Divide both sides by 70°F:

m2 = -212°F / 70°F ≈ -3.03 gallons

Since you can't have a negative volume of water, it suggests that it's not possible to cool a gallon of water at 212°F to 70°F using just one gallon of water. This result implies that more than three gallons of water at 70°F would be needed to cool down a gallon of water at 212°F.