Question

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?

Answer 1

Given, temperature `T_(A) = 12^(@)`C , `T_(B)= 19^(@)`C and `T_(C) = 28^(@)C` respectively.
When A and B are mixed, then from principle of calorimetery
`mc_(B))(19-16)`=`mc_(A)(16-12)`
`3c_(B) = 4c_(A) rArr c_(A) = 3/4c_(B)`
When B and C are mixed, then from principle of calorimeetry
`mc_(c)(28-23) = mc_(B)(23-19)`
`5c-9c = 4c_(B) rArr c_(c) = 4/5c_(B)`
When A and C are mixed, let hte equilibrium temperature be T. From principle of calorimetry common temperature of the mixture at equilibrium
`T = (mc_(c)T_(1) + mc_(A)T_(2))/(mc_(C) + mc_(A))`
`((4/5)c_(B)(28) + 3/4c_(B) xx 12)/(4/5c_(B) + 3/4c_(B))`
`=c_(B)(4/5 xx 28 + 3/4xx12)/(4/5+3/4)c_(B)`
`=(112/5)+9)/(16+15)/(20) = (1.12 +45)(20)/(31)xx5)`
`=(157 xx 20)/(155) = (3140)/(155) = 20.3^(@)C`