A total of 0.800 kg of water at 20 degrees celsius is places in a 1kw electric kettle. How long a time is needed to raise the temperture of water to 100 degrees celsius?

4.5mins

4.42 min

To calculate the time needed to raise the temperature of water, we can use the formula:

Q = mcΔT

Where:
Q is the amount of heat energy transferred (in Joules)
m is the mass of the water (in kilograms)
c is the specific heat capacity of water (approximately 4,186 J/kg°C)
ΔT is the change in temperature (final temperature - initial temperature, in degrees Celsius)

First, we need to calculate the amount of heat energy required to raise the temperature of 0.800 kg of water from 20°C to 100°C.

ΔT = 100°C - 20°C = 80°C

Q = (0.800 kg) * (4,186 J/kg°C) * (80°C)
Q = 268,416 J

Now, let's consider the electric kettle with a power rating of 1 kW (kilowatt). We know that power is defined as the amount of energy transferred per unit time. Therefore, we can use the power equation:

Power = Energy / Time

Since we want to find the time, we rearrange the equation:

Time = Energy / Power

Plugging in the values, we get:

Time = 268,416 J / 1,000 W

Converting watts to joules per second:

1 watt = 1 joule/second

Time = 268,416 J / 1,000 J/s
Time = 268.416 seconds

Therefore, it would take approximately 268.416 seconds or around 4.474 minutes to raise the temperature of the water from 20°C to 100°C in a 1 kW electric kettle.