The temperatures of equal masses of three different liquids A, B and C are `15^@C`, `20^@C` and `30^@C`, respectively. When A and B are mixed their equilibrium temperature is `18^@C`. When B and C are mixed, it is `22^@C` .What will be the equilibrium temperature when liquids A and C are mixed

Explanation

Let speficic heats of liquids are `s_(A),s_(B)` and `s_(C)` respectively. Then for mixing of liquids A and B we have
heat lost by B=heat gained by A
or `mxxs_(B)xx(20-18)=mxxs_(A)xx(18-15)`
`2s_(B)=3s_(A)` ..1.60
For mixing of liquid B and C we have
heat lost by C=heat gained by B
`mxxs_(C)xx(30-22)=mxxs_(B)xx(22-20)`
`8s_(C)=2s_(B)`
or `s_(B)=4s_(C)` ..............1.61
From equation 1.60 and 1.61 we get
`8s_(C)=3s_(A)` ......1.62
Now if liquids A and C are mixed, let the their equilibrium temperature in `T_(e)` then we have
Heat lost by C= heat gained by A
`mxxs_(C)xx(30-T_(e))=mxxs_(A)xx(T_(e)-15)`
or `(3s_(A))/8xx(30-T_(e))=s_(A)xx(T_(e)-15)`
or `90-3T_(e)=8T_(e)-120`
or `11T_(e)=210`
or `T_(e)=210/11=19.09.^(@)C`