hi i have sent back this question because i have not undertood where does it come 3.91 Kw? so that was 3.1KW. could please explain it ? If a...

Now we know that 1 W  is 1 J per second. 1kW = 1000 J /
s.

The capacity of the heater is 3.1 kW or 3.1 kJ /
s.

We need to increase the tempereature of 0.5 kg of water by 10
degree Celsius. The specific heat of water is given as 4200 J /
kg*K.

That means 4200 J or 4.2 kJ are required to increase the
temperature of 1 kg of water by 1 K.

We have to increase the
temperature of 0.5 kg of water by 10 degree Celsius, that is the same as increasing the
temperature by 10 K.

Therefore to do that, we need 4.2*0.5*10 kJ of
energy.

So the energy required is 21
kJ.

Now the heater produces 3.1 kJ of energy every second. To
produce 21 kJ of energy the time required is 21/3.1= 6.774
s

Therefore the answer is 6.77
s.