Energy Require from water-steam

[mom2maxncoop]

Homework Statement

How much energy is required to change one quarter of 8.0kg of water at 25°C into steam.

Homework Equations

I get confused to exact what equation to use to figure out the energy required.

I *think* it would be this one:
Q$_{t}$=M$_{water}$C$_{water}$$\Delta$T$_{water}$ + .25(M$_{water}$)L$_{f}$

The Attempt at a Solution

When I do the math, I come up with a ridulous number that makes no sense. I try and try to understand but I can't.

:/.

 

[gneill]

What are the values of the constants are you using? What value are you getting?

 

[mom2maxncoop]

Would it be:

Q=mc$\Delta$t
Q=(8.0kg)(4200J/(kg·°C))(100°C-25°C)
Q=2 520 000

Then since your finding a a quater of it would you then muliply by .25

2520000x.25

=630000J

It seems to easy since the question is worth 5 marks, it feels like I'm missing a step or something :/

 

[gneill]

It boils down to (pun!) whether you are expected to raise all 8.0 kg of water to 100° and then transform 1/4 of it to steam, or whether you are to take 1/4 of 8.0 kg of water and raise its temperature to 100° and then transform it to steam.

Your value for Q looks okay for raising the 8.0 kg of water to 100°. How much additional energy will it take to convert 1/4 of that water at 100° to steam at 100°?

 

[mom2maxncoop]

I loved the pun, I actually had a giggle with that one!

Right now I'll have to find the mass of the steam itself!
Q=

To find the additional energy would I use the equation that I initially posted (would I use latent fusion or Latent vaporiztion)?

BUT I don't know the mass of the steam nor do I know the Energy, so I have NO Idea where to go next :(:(

(it sucks trying to teach yourself everything from Grade 11 math when you've been out of high school for 6 years :/)

 

[gneill]

The mass is just 1/4 of 8.0 kg. You want to vaporize this mass of water, so you'd use the latent heat of ______?

 

[mom2maxncoop]

Vaporization since you want to vaporize the mass.

So with that being said

Q=(8.0kg)(4200J(kg·°C)(100°C-25°C)+.25(8.0kg)(2300000)
Q=2520000 + 4600000
Q=7120000J

 

[gneill]

Looks good!

 

[mom2maxncoop]

Thank you so much!