An electric kettle rated accurately at 2.5kw is used to heat 3kg of water from 15% to boiling point it takes 9.5 minute. Then the amount of heat that has been lost is

power=heat/time=3kg*4.18kJ/kg*(100-15)/9.5*60

so power into water then is 3*4.18*85/9.5*60=1.87 kw

so the power lost is 2.5-1.87 kw
and heat lost=powerlost*9.5*60 kiloJoules

The temperature must be in deg C if using water's specific heat capacity of 4.18 kJ/(kg*C).

Heat absorbed by water
= 3kg * 4.18 kJ/(kg*C) * (212 C - 15 C)
= 2470.38 kJ

Heat created by 2.5 kW kettle in 9.5 minutes
= 2.5 kJ/s * (9.5 min * 60 s/min)
= 1425 kJ

This question doesn't make sense then, because the kettle can't even produce enough heat for what the water requires to boil it.

To calculate the amount of heat lost, we need to determine the amount of heat required to heat the water from 15% to boiling point first.

First, let's calculate the initial temperature of the water:
Initial temperature (Ti) = 15% of boiling point
Boiling point of water = 100 degrees Celsius
Ti = 0.15 * 100 = 15 degrees Celsius

Next, let's calculate the final temperature of the water:
Final temperature (Tf) = boiling point = 100 degrees Celsius

The amount of heat required to heat the water can be calculated using the formula:

Q = m * C * (Tf - Ti)

Where:
Q = amount of heat
m = mass of water
C = specific heat capacity of water
Tf = final temperature
Ti = initial temperature

Given:
m = 3 kg
C = 4.186 J/g°C (specific heat capacity of water)

Converting mass from kg to g:
m = 3 kg * 1000 g/kg = 3000 g

Substituting the values into the formula:

Q = 3000 g * 4.186 J/g°C * (100°C - 15°C)

Q = 3000 g * 4.186 J/g°C * 85°C

Q = 900,645 J

Now, let's calculate the amount of heat lost.

The electric kettle is rated at 2.5 kW, which means it can generate 2,500 Joules of heat per second (since 1 kW = 1,000 J/s).

The time taken to heat the water is 9.5 minutes, which is equal to 9.5 * 60 seconds = 570 seconds.

The amount of heat generated by the kettle is:
Heat generated = Power * Time
Heat generated = 2,500 J/s * 570 s
Heat generated = 1,425,000 J

Therefore, the amount of heat lost is:
Heat lost = Heat generated - Heat required
Heat lost = 1,425,000 J - 900,645 J
Heat lost = 524,355 J

Therefore, the amount of heat lost is 524,355 Joules.

To find the amount of heat that has been lost, we need to calculate the amount of heat gained by the water and subtract it from the total amount of heat supplied by the electric kettle.

First, let's calculate the amount of heat gained by the water. We can do this using the formula:

Q = mcΔT

Where:
Q is the amount of heat (in joules)
m is the mass of the water (in kilograms)
c is the specific heat capacity of water (approximately 4200 J/kg°C)
ΔT is the change in temperature (in degrees Celsius)

Given:
Mass of water (m) = 3 kg
Change in temperature (ΔT) = (100 - 15) = 85°C
Specific heat capacity of water (c) = 4200 J/kg°C

Q = (3 kg)(4200 J/kg°C)(85°C)
Q = 1,130,500 J

Next, let's calculate the total amount of heat supplied by the electric kettle. We can do this using the formula:

Total heat supplied = Power x Time

Given:
Power (P) = 2.5 kW = 2500 W
Time (t) = 9.5 minutes = 9.5 minutes x 60 seconds/minute = 570 seconds

Total heat supplied = (2500 W)(570 seconds)
Total heat supplied = 1,425,000 J

Finally, we can find the amount of heat lost by subtracting the amount of heat gained by the water from the total amount of heat supplied by the electric kettle:

Heat lost = Total heat supplied - Heat gained by water
Heat lost = 1,425,000 J - 1,130,500 J
Heat lost = 294,500 J

Therefore, the amount of heat lost is 294,500 Joules.