Question:The temperature of equal masses of three different liquids A,B and C are 12 degree C ,19 degree C and 28 degree C respectively.The temperature ,when A and B are mixed ,is 16 degree C, and when B and C are mixed,is 23 degree C.what will be the temperature when A and C are mixed ?

Dear student
 
Let a, b and c be the specific heat capacities of liquids A, B and C.
Let the mass of the liquids be m.
When A and B are mixed:
ma (16-12) = mb(19-16)
4a = 3b
When B and C are mixed:
mb(23-19)= mc(28-23)
4b = 5c
Therefore, 16a = 12b = 15c
Let x be the temperature when A and C are mixed
ma(x-12) = mc(28-x)
a/c = 15/16 = (28 -x) /(x-12)
15x -180 = 448 -16x
31x = 628
x = 20.25 °c

Regards
Arun (askIITians forum expert)