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

Let m be the mass of eac liquid and `S_(A),S_(B),S_(C)` be specific heats of liquids A,B and C respectively.When A and B are mixed. Th final temperature is `16^(@)C`.
`:.` Heat gained by A=heat lost by B
i.`mS_(A)(16-12)=mS_(B)(19-16)`
i.e. `S_(B)=4/3S_(A)`.............(i)
When B and C are mixed. Heat gained by B=Heat lost by C
i.e. `mS_(B)(23-19)=mS_(C)(28-23)`
i.e. `S_(C)=4/5S_(B)` ..............(ii)
From eq. (i) and (ii)
`S_(C)=4/5xx4/3 S_(A)+16/15S_(A)`
When A and C aremixed let the final temperature be `theta`
`:.mS_(A)(theta-12)=mS_(C)(28-theta) `
i.e. `theta-12=16/15(28-theta)`
By solving we get
`theta=628/31=20.25^(@)C`