Final answer:
The boiling heat transfer coefficient is calculated using the provided power consumption of the electric wire and the temperature difference between the wire surface and the water. By determining the surface area of the wire and applying the formula for heat transfer coefficient, we find the correct value among the given options.
Step-by-step explanation:
To determine the boiling heat transfer coefficient of water at 1 atm with a submerged electric resistance wire, we use the power supplied to the wire and the temperature difference between the wire surface and the boiling water. The power consumption of the wire is given as 4.1 kW (which is equal to 4100 J/s), and the wire has a surface temperature of 130°C, while the boiling point of water at 1 atm is 100°C.
The first step is to calculate the heat transfer per unit time, which is simply the power consumption, as the heat is directly being used to heat the water. To calculate the heat transfer coefficient (α), we will use the equation α = Q / (A * ΔT), where Q is the heat transfer per unit time, A is the surface area of the wire, and ΔT is the temperature difference between the wire surface and the boiling water.
Firstly, we need to find the surface area of the wire: A = π * d * L, where d is the diameter, and L is the length of the wire. Substituting 0.2 cm for d and 50 cm for L, we get A = π * 0.002 m * 0.5 m.
Next, using the temperature difference ΔT = 130°C - 100°C, the heat transfer coefficient (α) can be calculated. After computing the values, using α = Q / (A * ΔT), we can find which option (a, b, c, d, or e) correctly represents the heat transfer coefficient.