Achieve homework question 9

[Xinyue Zou 2K]

Hello!
I've gone over our lecture notes on specific heat capacity but I don't think we went over how to find final temperature, or if we did I forgot to jot it down. I also don't really understand how to manipulate the equations pertaining to this question.... Could someone give me some direction on how to approach this problem? I've pasted it below:

If you combine 380.0 mL of water at 25.00 C and 120.0 mL of water at 95.00 C, what is the final temperature of the mixture? Use 1.00 g/mL as the density of water. (The chart says the specific heat of liquid water is 4.184)

Thank you!

[Noah Ho 1F]

When you combine two liquids at different temperatures, the final temperature will be somewhere between these 2 temps. You don't know what this final temperature is so you don't know what delta H is. However, you know what the specific heat capacity of water is and you can find the mass of each liquid. We also know that the higher temp water will release energy and that the lower temp water will gain the same amount of energy because conservation of energy. Thus, we can set c1*m1*(Tfinal-Tinitial)=c2*m2*(Tfinal-initial) and find the final temperatures.

[Xinyue Zou 2K]

When you combine two liquids at different temperatures, the final temperature will be somewhere between these 2 temps. You don't know what this final temperature is so you don't know what delta H is. However, you know what the specific heat capacity of water is and you can find the mass of each liquid. We also know that the higher temp water will release energy and that the lower temp water will gain the same amount of energy because conservation of energy. Thus, we can set c1*m1*(Tfinal-Tinitial)=c2*m2*(Tfinal-initial) and find the final temperatures.

For the equation c1*m1*(Tfinal-Tinitial)=c2*m2*(Tfinal-initial), how do we set it up in order to find Tfinal?
I currently have it arranged as (4.184)(380 g)(Tfinal - 25 C) = -(4.184)(120 g)(Tfinal - 95 C) and once I solved it for Tfinal I got Tfinal = 7.3, however that's clearly not correct haha.
Thank you!

[Noah Ho 1F]

I set it up as (380)(4.184)(Tf-25)=120(4.184)(95-x). Sorry. I think I made a mistake when I set up the equation the first time. For the water with the higher temp, you can do initial temp-final temp.

[Xinyue Zou 2K]

I set it up as (380)(4.184)(Tf-25)=120(4.184)(95-x). Sorry. I think I made a mistake when I set up the equation the first time. For the water with the higher temp, you can do initial temp-final temp.

Thank you so much! I solved it :) If you don't mind, could you explain why the higher temperature would become (initial temp - final temp) and why the negative sign is gone from the right side of the equation? In the Achieve feedback they gave us the equation as m(cold water)(c)(delta T) = -m(hot water)(c)(delta T) so I'm wondering how you knew to change it the way you did.