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 will be the temperature when `A` and `C` are mixed ?

Answer

B, C

Explanation

Given , The temperature of `A = 12^(@)C`
The temperature of `B = 19^(@)C`
The temperature of `C= 28^(@)C`
`rArr` The temperature of `A + B= 16^(@)C`
`rArr`The temperature of `B + C = 23^(@)C`
In accordance with the principal of calorimetry, when A and B are mixed
`M_(CA) (16- 23) = M_(CB)(19 - 16)`
`rArr 4M_(CA)=3M_(CB)`
`rArr M_(CA)=((3)/(4))M_(CB)`
and when B and C are mixed
`M_(CB) (23 - 19) = M_(OC) (28 - 23)`
`rArr 4M_(CB)=5M_(OC)`
`rArr M_(OC)=((4)/(5))M_(CB)`
When A and C mixed, If T is the common tempetature of the mixture
`M_(CA) (T - 12) = M_(OC) (28 - T)`
`rArr ((3)/(4))M_(CB)= (T - 12) = ((4)/(5))M_(CB)(28 - T)`
`rArr ((3)/(4))(T - 12) = ((4)/(5))(28 - T)`
`rArr (3 xx 5) (T - 12) = (4 xx 4) (28 - T)`
`rArr 15T =T - 180= 448 - 16T`
`rArr 31T = 628`
`rArr T = (628)/(31) = 20.253^(@)C`
`= 20.3^(@)C`