Heating 5.0dl of Coffee Water: How long does it take?

[chawki]

Homework Statement

Coffee maker, whose output of 650 W, producing coffee. Kettle to the boil 5.0 dl of water, with an initial temperature of 14 ° C. Heat capacity of water is 4.19 kJ / (kg ° C) and water density of 1.0 kg/dm3

Homework Equations

How long does it take a coffee water heating, if the stove efficiency is 92%?

The Attempt at a Solution

m=0.5kg
Cp=4.19kj/kg*C
density of water=1000kg/m³
P=650Watt

efficiency=92%=0.92
Q/E=0.92
E=Q/0.92

Q=m*Cp*delta T
Q=0.5*4.19*14
Q=29.33Kj

E=Q/0.92
E=29330/0.92
E=31880.43 J

P=E/t (why here we don't use P=Q/t)
t=E/P
t=31880.43/650
t=49.04 s

 

[gneill]

E=Q/0.92
E=29330/0.92
E=31880.43 J

P=E/t (why here we don't use P=Q/t)
t=E/P
t=31880.43/650
t=49.04 s

You don't use P = Q/t because the coffee maker is not 100% efficient. Q is the joules required to raise the temperature of the water to the required point, but the energy E being generated by the stove is not all going into the water, some of it is escaping elsewhere. Even so, it's the energy that the stove produces that you need to 'meter' for time.

You worked out that the stove needs to produce E joules in order for amount Q of it to end up in the water.

 

[chawki]

Ah now i get it...so when they don't give E, it's probably because the stove is 100% efficient and thus E=Q !

 

[chawki]

Is my answer correct?

 

[gneill]

I didn't do the math, but the method looks fine.