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 is $$16$$∘C, when B and C are mixed is $$23$$∘C , what is the temperature when A and C are mixed?

Question

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 is  $$16$$∘C, when B and C are mixed is $$23$$∘C , what is the temperature when A and C are mixed?

Infinity Learn · Accepted Answer

Case $$1$$: When A and B mixed $$Resultant=$$ $$16ocapply$$ principle of method of mixtures, heat lost by hot body $$B=$$ heat gained by cold body Aheat lost or gain $$=$$ $$MS(temperature$$ $$difference)$$,where M is mass of the body , S is specific heat of the bodyheat gain by $$A=$$ heat lost by B,  here common temperature is $$160C$$ $$MS1$$[$$16-12$$]$$=MS2$$[$$19-16$$]$$S2=43S1----(1)Case$$ $$2$$: When B and C mixedheat gain by B $$=$$ heat lost by C. here common temperature is $$23$$ $$CMS2$$[$$23-19$$]$$=MS3=$$[$$28-23$$]$$4S2=5S3substitute$$ equation (1)4$$×$$43S1=5S3S3=1615S1----(2)Case$$ $$3$$: When A and C are mixedheat gain by A $$=$$ heat lost by $$CMS1$$[$$T-12$$]$$=MS3$$[$$28-T$$]substitute equation $$(2) $$S1$$[$$T-12$$]$$=1615S1$$[$$28-T$$]$$T=20.26octhis$$ is the temperature when A and C are mixed

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