Question 2: 2pts) We want to predict the final temperature of a mixture of hot a

Question

Question 2: 2pts) We want to predict the final temperature of a mixture of hot and cold water. Starting from equation 3, symbolically determine the final temperature of the mixture without plugging in any numbers. Your answer should be in terms of the mass of the cold water (m1), the mass of the hot water (m2), the initial temperature of the cold water (Ti1), and the initial temperature of the hot water (Ti2). Note that since the two materials we are mixing are both water, they should have the same specific heat (c cs water). Be sure to show all your work and box your answer.

Explanation / Answer

We know that, heat transfer can be given as:

Q= mcT

We are dealing with hot and cold water mixture,

Heat rejected by hot water will be equal to heat accepted by cold water .

Final temperature will be attained upon equilibrium hence

For hot water: Q = mhch(ti-tf) here mh is mass of hot water while ch is heat capacity.

For cold water Q= mccc(tf-ti) , mc is mass of cold water and cc is heat capacity.

Since, ch=cc = c

We have

Mh(ti-tf)+ Mc(tf-ti)=0 [ we took c ,as common hence canceled out]

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