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 specific heat of liquid A, B and C are `s_A`,`s_B` and `s_C` resprectively.
When A and B are mixed,
`ms_B(19-16)=ms_A(16-12)`
`3s_B=4s_Aimpliess_A=(3)/(4)s_B`
When B and C are mixed,
`ms_C(28-23)=ms_B(23-19)`
`5s_c=4s_Bimpliess_C=(4)/(5)s_B`
When A and C are mixed, let equilibrium temperature be `theta`
`ms_C(28-theta)=ms_A(theta-12)`
`(4)/(5)s_B(28-theta)=(3)/(4)s_B(theta-12)`
`16(28-theta)=15(theta-12)`
`448-16theta=15theta-180`
`31theta=628`
`theta=(628)/(31)=20.3^@C`