the heating element of a coffee maker operates at 120 V and carries a current of 2 A. Assuming that the water absorbs all of the energy converted by the resistor, calculate how long it takes to heat .500 kg of water from room temperature 23 degrees C to the boiling point.

11.2 min

To calculate the time it takes to heat the water from room temperature to boiling point, you can use the formula:

Q = mcΔT

Where:
Q is the amount of heat energy required (in Joules)
m is the mass of the water (in kg)
c is the specific heat capacity of water (approximately 4.18 J/g°C)
ΔT is the change in temperature (in °C)

First, we need to convert the mass of water from grams to kilograms:
0.500 kg = 500 g

The change in temperature (ΔT) is the final temperature minus the initial temperature:
ΔT = boiling point temperature - room temperature
ΔT = 100°C - 23°C
ΔT = 77°C

Now, let's calculate the amount of heat energy required (Q):
Q = mcΔT
Q = 500 g × 4.18 J/g°C × 77°C
Q = 192,550 J

We can now calculate the time (t) required using Ohm's law:
P = VI

Where:
P is the power (in Watts)
V is the voltage (in Volts)
I is the current (in Amperes)

The power (P) can be calculated as:
P = VI
P = 120 V × 2 A
P = 240 W

Finally, we can calculate the time (t) using the formula:
t = Q / P

t = 192,550 J / 240 W
t ≈ 802.3 seconds

Therefore, it takes approximately 802.3 seconds (or about 13 minutes and 22 seconds) to heat 0.500 kg of water from 23°C to the boiling point.