Final answer:
To find the resistance of a heater at 100°C, we need to calculate the heat required to raise water's temperature, the power used by the heater, and then use these values to solve for resistance using Ohm's law.
Step-by-step explanation:
To calculate the resistance of the heater, we can apply the formula Q = mcΔT, where Q is the heat added, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. The power used by the heater, P, can then be calculated using P = Q/t, where Q is the heat added from the previous calculation and t is the time. Knowing that P = V^2/R, where P is the power, V is the voltage, and R is the resistance, we can solve for the resistance, R.
First, calculate the heat needed to raise the temperature of the water:
- Q = mcΔT = 0.400 kg × 4180 J/kg°C × (100°C - 25°C)
Then calculate the power used during the heating:
- P = Q/t = (Q from the previous step) / (2 × 60 s)
Finally, calculate the resistance of the heater:
- R = V^2/P = (115.00 V)^2 / (P from the previous step)
After doing the math, we would obtain the value for the resistance at 100°C.