Specific heat and possibly latent heat too..

[shannon.leigh]

Homework Statement

0.5kg of ice at 0 degrees celcius is mixed with 0.1kg of steam at 100 degrees celcius. what will be the final temperature?

Homework Equations

delta Q= m*c*delta T

and at first i thought delta Q= m*Lf ,but then i changed my mind. . .

The Attempt at a Solution

In my first attempt, i went

Lf*m(of ice) + m*c*(Tf-Ti)(of the now liquid water)=Lv*m(of steam)+ c*m*(Tf-Ti)(of now liquid water)

so 3.34*10^5*0.5 +0.5*4200*(T-0)=2.26*10^6*0.1+4200*0.1*(100-T)
167000+2100T=226000+42000-420T
2520T=435000
T=435000/2520
=172.62
Which is wrong!

so then i got rid of the latent heat and fusion, because i thought they were irrelevant to what i was trying to figure out and went
2100T=42000-420T
T=42000/2520
=16.67
Which is still wrong!

HELP ME PLEASE!

thankyou (:

 

[ehild]

167000+2100T=226000+42000-420T
2520T=435000

Do the simplification again, the RHS is not 435000.

ehild

 

[shannon.leigh]

Are you serious? I just screwed up the calculations?
Damn my terrible skills with a calculator!
And thankyou thankyou thankyou for pointing that out ehild!
I am forever in your debt. :)

 

[ehild]

To tell the truth, there was a mistake in your equation, but you proceeded all right till the last row.

"Lf*m(of ice) + m*c*(Tf-Ti)(of the now liquid water)=Lv*m(of steam)+ c*m*(Tf-Ti)(of now liquid water)"

The red text should be Ti-Tf.

ehild

 

[rwisz]

Dear student,

It seems like you are on the right track, but there are a few things to consider in order to arrive at the correct answer.

First, when solving for the final temperature, you need to make sure that you are using the correct units for each variable. In this case, the specific heat capacity (c) should be in units of J/kg°C, the mass (m) should be in kilograms, and the change in temperature (delta T) should be in degrees Celsius.

Second, it's important to keep track of the state of the substance throughout the calculation. In this case, we have ice (solid) and steam (gas) at different temperatures, so we need to account for the energy required to change their states as well as the energy required to change their temperatures.

With these considerations in mind, here is the correct approach to solving this problem:

1. Calculate the energy required to melt the ice: Q = m * Lf, where m is the mass of ice and Lf is the latent heat of fusion for water (3.34 x 10^5 J/kg).

2. Calculate the energy required to raise the temperature of the melted ice to the final temperature: Q = m * c * delta T, where m is the mass of the melted ice, c is the specific heat capacity of water (4200 J/kg°C), and delta T is the change in temperature from 0°C to the final temperature.

3. Calculate the energy required to vaporize the steam: Q = m * Lv, where m is the mass of steam and Lv is the latent heat of vaporization for water (2.26 x 10^6 J/kg).

4. Calculate the energy released by the steam as it condenses: Q = m * Lv, where m is the mass of steam and Lv is the latent heat of vaporization for water.

5. Set these two calculations equal to each other and solve for the final temperature.

I hope this helps! Let me know if you have any further questions.