Temperature of the Lower Surface of the Pot in Contact with the Stove

To determine the temperature of the lower surface of the pot in contact with the stove, we need to consider the heat transfer that occurs between the hot stove and the pot.

Heat Transfer Mechanism
Heat is transferred through conduction from the stove to the pot. Conduction is the transfer of heat through direct contact between two objects or substances. In this case, the stove and the pot are in direct contact, allowing heat to flow from the stove to the pot.

Conduction Equation
The rate of heat transfer through conduction can be calculated using the following equation:

Q = k * A * ΔT / d

where:
Q is the rate of heat transfer (in watts),
k is the thermal conductivity of the material (in watts per meter per degree Celsius),
A is the area of contact between the stove and the pot (in square meters),
ΔT is the temperature difference between the stove and the pot (in degrees Celsius),
and d is the thickness of the pot's steel bottom (in meters).

Calculating the Rate of Heat Transfer
Given the area of the pot's bottom (0.15 m²) and the thickness of the steel bottom (1.2 cm = 0.012 m), we can calculate the rate of heat transfer.

Assuming the stove is at a higher temperature than the pot, let's say the stove temperature is Ts and the pot temperature is Tp.

ΔT = Ts - Tp

Calculating the Mass of Water Vaporized
We are given that 0.44 kg of water vaporizes every 5 minutes. To find the rate of mass transfer, we divide the mass by the time:

m = 0.44 kg
t = 5 minutes = 300 seconds

Rate of mass transfer = m / t = 0.44 kg / 300 s

Heat Transfer and Mass Transfer Relationship
The heat required to vaporize a certain mass of water can be calculated using the latent heat of vaporization (Lv). The relationship between the heat transfer and the mass transfer is given by:

Q = m * Lv

Calculating the Temperature of the Lower Surface of the Pot
To find the temperature of the lower surface of the pot, we need to equate the rate of heat transfer to the rate of mass transfer:

k * A * ΔT / d = m * Lv / t

Rearranging the equation, we can solve for ΔT:

ΔT = (m * Lv * d) / (k * A * t)

Substituting the given values, we can calculate the temperature difference:

ΔT = (0.44 kg * Lv * 0.012 m) / (k * 0.15 m² * 300 s)

By solving this equation, we can determine the temperature difference between the stove and the pot. The temperature of the lower surface of the pot can then be calculated by subtracting the temperature difference from the stove temperature (Ts - ΔT).