Efficiently Heat Soup: Calculate Time Needed with 350W Immersion Heater

[iheartpink]

I know this is a simple problem, but I don't know where to begin.
Please help!

A small immersion heater is rated at 350W. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 15 degrees celsius to seventy-five degrees celsius

 

[hage567]

What do you know about heat capacity? What is the definition of power?

 

[iheartpink]

i know that power is the change of work divided by the change in time. the problem is asking for the time so i need to solve for the change of work. the change in work isn't as simple as the difference in temperature, right?

 

[iheartpink]

can some one help me with this problem. i am stuck. i don't know where to go from here...

 

[dst]

It takes a certain amount of energy to heat a volume of water up 1 degree celsius. That energy is "specific heat capacity". Work from there.

In this case, you're using volumetric heat capacity which Wiki defines as 4.181 joules per cubic centimetre per kelvin for water at 25*C.

You have to:

1.) Convert all the given units into standard units (mL = cm^3)

2.) Work out the energy needed to heat that volume of water to that temperature

3.) Calculate how long it will take for the 350W (joules per second) heater to give out energy equal to the amount needed for the water.