The temperature of equal masses of three different liquids A, B and C are 12∘C,19∘C and 28∘C respectively. The temperature when A and B are mixed is16∘C and when B and C are mixed is 23∘C. What should be the temperature (in 0C ) when A and C are mixed?

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answer is 20.26.

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Detailed Solution

Given TA=12∘C,TB=19∘C and TC=28∘C. Let CA,CB and CC are the specific heats of respective liquids. When liquid A and B are mixed, the temperature of mixture becomes 160C, thenmCA(16−12)=mCB(19−16) or CB=43CA......(i) When liquid B and C are mixed, the temperature of mixture becomes 23∘C , then mCB(23−19)=mCC(28−23) or CB=54CC...........(ii) From (i) and (ii), we get CA=1516CC Now when A and C are mixed, let equilibrium temperature of mixture is T , then mCA(T−12)=mCC(28−T) or 1516CC(T−12)=CC(28−T) 31T=628 or T=20.26∘C .

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