Final answer:
The time taken to heat the water using a 230.0 W immersion heater is approximately 3.54 minutes.
Step-by-step explanation:
To find the time taken to heat the water, we can use the formula:
Q = mcΔT
where Q is the heat absorbed by the water, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
First, let's calculate the heat absorbed:
Q = (160.0g)(4.18 J/g°C)(82.0°C - 12.50°C) = 48,744 J
Next, let's use the power of the heater to find the time taken:
Power = ΔQ / t
where Power is the power of the heater, ΔQ is the change in heat absorbed, and t is the time taken.
Rearranging the formula, we get:
t = ΔQ / Power
Plugging in the values, we get:
t = 48,744 J / 230.0 W = 212.36 seconds
Converting seconds to minutes, we get:
t ≈ 3.54 minutes