Resistance of a water heaters heating element?

[Rijad Hadzic]

Homework Statement

Household water heaters use a 240 V rather than a 120 V source. What is the resistance of a water heater's heating element if it heats 40 gallons (151 kg) of water from 15 C to 60 C in 15 min

Homework Equations

P = IV
P = I^2R
I = dq/dt

The Attempt at a Solution

Honestly no clue. If anyone can give me some hints I would really appreciate this.

So far I have electrical units, V, and then I have kg, Celcius, and seconds. I'm not sure how the given equations help me relate the units at all.

I need current and power, but those units do not help me at all.

I know I = dq/dt, and I thought 45 C / 900 s looks very similar to current but the units don't make sense to me...

 

[Chestermiller]

Do you know how to determine how much heat it takes to raise the temperature of 1 kg of water from 15 C to 60 C?

 

[Rijad Hadzic]

Do you know how to determine how much heat it takes to raise the temperature of 1 kg of water from 15 C to 60 C?

I'm not sure actually.. this chapter that I'm studying is called Current and Resistance..

It has to do with specific heat, right? Also, does heat = thermal energy?

 

[Chestermiller]

I'm not sure actually.. this chapter that I'm studying is called Current and Resistance..

It has to do with specific heat, right? Also, does heat = thermal energy?

Yes. Did you not study heat in freshman physics?

 

[Rijad Hadzic]

Yes. Did you not study heat in freshman physics?

I don't think I studied it enough..

So if the specific heat of water is 4.187 x 10^3 J/(kg * k )

That means it requires 4.187 x 10^3 J to raise 1 kg of water by 1 kelvin, correct?

 

[scottdave]

I'm not sure actually.. this chapter that I'm studying is called Current and Resistance..

It has to do with specific heat, right? Also, does heat = thermal energy?

Yes, heat = thermal energy. To raise a kg water 1°C, you need 4184 Joules of heat (thermal energy).

http://www.kentchemistry.com/links/Energy/SpecificHeat.htm

 

[Chestermiller]

What is the mass in kg of 40 gallons of water?

 

[Cluemore]

What is the mass in kg of 40 gallons of water?

I think the asker had the converted number already [emoji846]. They wrote 151 kg.

 

[Cluemore]

Anyhow, using the heat you can now calculate the power (J/s). See that the heat is the 'J' and the time you have the 's'.

Now think about how you can get current!