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` and when B and C are mixed it is `23^@C`. What should be the temperature when A and C are mixed?

Explanation

Given `T_(A) = 12^(0)C, T_(B) = 19^(0)C and T_(C) = 28^(0)C`
Let `C_(A), C_(B) and C_(C)` are the specific heats of respective liquids.
When liquid A and B are mixed, the temperature of mixture becomes `16^(0)C`, then
`mC_(A) (16 - 12) = mC_(B) (19 -16) (or) C_(B) = 4/3C_(A)` ...... (i)
When liquid B and C are mixed, the temperature of mixture becomes `23^(0)C`, then
`mC_(B) (23 -19) = mC_(C) (28- 23) or C_(B) = 5/4 C_(C)` ...... (ii)
From (i) and (ii), we get `C_(A) = (15)/(16)C_(C)`
Now when A and C are mixed, let equilibrium temperature of mixture is T, then
`mC_(A) (T - 12) = mC_(C) (28-T) (or) 15/16 C_(C) (T -12) = C_(C) (28 - T) 31 T = 628 or T = 20.26^(0)C`