InterviewSolution
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The temperatures of equal masses of three different liquids A, D and C are `12^@C`,`19^@C` and `28^@C`, respectively. The temperature when A and B are mixed is `16^@C`, while when B and C are mixed, it is `23^@C`. What would be the temperature when A and C are mixed? |
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Answer» Let `m=`mass of each liquid, when A and B are mixed, Heat lost by `B=` heat gained by A `impliesmS_B(19-16)=mS_A(16-12)implies2S_B=4S_A` …(i) When B and C are mixed, Heat lost by `C=` heat gained by B `impliesmS_C=(28-23)=mS_B(23-19)implies5S_C=4S_B` .(ii) From eqs. (i) and (ii), we get `16S_A=12S_B=15S_C` ..(iii) When A and C are mixed, Let `theta=`final temperature Heat lost by `C=` heat gained by A `impliesmS_C=(28-theta)=mS_A(theta-12)` Using Eq. (iii), we get `implies15S_C(28-theta)=15S_A(theta-12)` `implies16S_A(28-theta)=15S_A(theta-12)` On solving for `theta`, we get `theta=(16xx28+12xx15)/(16+15)` `impliestheta=20.26^@C` |
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