Heat and adiabatic processes perhaps

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The discussion revolves around calculating the final temperature of two mixed water samples in an insulated thermos, emphasizing that the process is adiabatic. The initial temperatures and masses of the water samples are provided, with one at 42.32°C and the other at 21.34°C. The proposed formula for the final temperature is Tf = [(m1*T1) + (m2*T2)] / (m1+m2), which is appropriate for this scenario. Participants express uncertainty about the problem-solving approach but confirm the adiabatic nature of the process. Understanding this calculation is essential for accurately determining the final temperature of the mixed water.
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You have two cups, one with m1 = 2.73 kg of water at t1 = 42.32oC and the other with m2 = 1.88 kg at t2 = 21.34oC. You mix the two in an insulated thermos. What is the final temperature of the water?

I'm pretty sure that this is supposed to be an adiabatic process, because you are trying to keep all of the temperature from going into the outside environment. However, i have absolutely no idea as to how to go about doing this problem.
 
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Is there a certain equation that I am supposed to use?
 
Tf = [(m1*T1) + (m2*T2)] / (m1+m2)

Hope this helps! :)
 

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