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Question

The temperatures of equal masses of three different liquids A,B and C are 12C,19C and 28C respectively. The temperature when A and B are mixed is 16C, when B and C are mixed is 23C. What is the temperature when A and C are mixed?

A
31C
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B
20.26C
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C
19.5C
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D
28C
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Solution

The correct option is B 20.26C
Let m be the mass of each liquid. Let the specific heats of A,B and C be s1,s2 and s3 respectively.
(i) When A and B are mixed:
Heat gained by A= Heat lost be B
ms1(1612)=ms2(1916)
or s2=43s1...(i)

(ii) When B and C are mixed:
Heat gained by B= Heat lost be C
ms2(2319)=ms3(2823)
4s2=5s3
s3=45s2=45×43s1=1615s1...(ii)

(iii) When A and C are mixed:
Let θ be the resultant temperature.
Heat gained by A= Heat lost by C
ms1(θ12)=ms3(28θ)
or s1(θ12)=s3(28θ)=1615s1(28θ)
θ=62831=20.26C

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