Calculating Heat Transfer and Latent Heat

[sin_city_stunner]

Hey all,
i got a problem I am stuck with and it'll probably be easy for you but i can't figure it out for some reason... It has to do with heat transfer and latent heat...

A tank containing 740 kg of water cools from 15 degrees to 0 degrees and completely freezes. What is the total heat given off? How many hours would a 1.2 kW eletric heater have to work to provide the equivilant heat the water gives off? (The heater provides 1.2 x 10^3 J/s of heat)

thanks

heres my work:

for part 1: Q=mcT
Q= (740kg)(4200 J/ kg C)(0 degrees- 15 degrees) 9specific heat capacity for water= 4200 J/kg C
= -46 620 000 J

Q= LfM
Q= (3.3x10^5 J/kg)(740 kg)
Q= 244 200 000 J

Total heat= -46 620 000J + 244 200 000J
=197 580 000

book says answer is 2.9 x 10^8 (with S.d.) I know how to do the second part but its this first part messing me up...

 

[Päällikkö]

What's the minus sign for? Why doesn't the answer from the second equation have a minus?

 

[sin_city_stunner]

the minus sign is there because deltaT is equal to : final temperature-initial temperature...which in the first part is 0-15...there is no negative sign in the second part because the delta T is positive

 

[Päällikkö]

In the second part (referring to Q = LfM), if the water didn't freeze, but melt, how would the equation show it (where would the plus/minus sign come from)?

 

[sin_city_stunner]

its the same regardless because the energy will be the same whether you are freezing or melting the object...

 

[Päällikkö]

Umm.. No. You're now saying that freezing and melting both bind energy (as in opposite to give off).
There's a difference between you heating water from 0 to 15 degrees and cooling from 15 to 0.

Thus, there must be a minus sign in the equation Q = LfM, when something freezes (logically it gives off energy).

 

[sin_city_stunner]

really? that must be the problem then...my teacher never taught us about a negative sign...he just said use this equation and plug in the numbers... sigh...thanks for your help BTW