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A 40-gallon electric water heater has a 10kW heating element. What will the water temperature be after 15 min of heating if the start temp is 50F degrees.

There must be an equation. I can't find it in notes or text.

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closed as too localized by David Z Jan 23 '12 at 20:29

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do you know what the definition of a Watt (W) is? You will get more answers when you detail where you are stuck. –  luksen Jan 23 '12 at 17:56
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what does this have to do with renewable energy? And what's with the caps? -1 –  user2963 Jan 23 '12 at 18:36
    
Hi Johnny, and welcome to Physics Stack Exchange! As stated in our FAQ, this is not really a homework help site, and just asking for the equation you need to answer your problem isn't the kind of question that is appropriate here. –  David Z Jan 23 '12 at 20:31
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1 Answer 1

You need to know these things to solve the problem:

  • Power of the heater is the rate at which energy is exchanged:

\begin{equation} P = \frac{dW}{dt} \end{equation}

where W is energy (here: the amount of electric energy transformed into heat by the heater), P power (here: of the heater) and t time.

  • Specific heat capacity is the amount of heat energy that needs to be transferred to a unit of mass of a given substance in order to increase its temperature by a degree.

\begin{equation} c_w = \frac{1}{m} \frac{Q}{\Delta T} \end{equation}

where cw is specific heat capacity of substance w (here: water), m is the mass of the the heated substance, Q heat transferred and T temperature.

In your assignment heater has constant power so the first derivative can be replaced by difference quotient.

You can use the first equation to calculate the amount of heat transferred from the heater to water and the second equation to calculate the effect the heat has on water in terms of temperature change.

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