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Question

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

A

30.26C

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B

40.26C

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C

20.26C

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D

10.26C

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Solution

The correct option is C

20.26C


Let m be the mass of each liquid.

When A and B are mixed,
Heat lost by B = Heat gained by A
msBΔTB=msAΔTA
sB(1916)=sA(1216)
3sB=4sA . . . .(1)

When B and C are mixed,
Heat lost by C = Heat gained by B
msCΔTC=msBΔTB
sC(2823)=msB(1923)
5sC=4sB . . . .(2)

From (1) and (2), we get:
16sA=12sB=15sC . . . .(3)

When A and C are mixed,
Let θ be the final temperature attained
Heat lost by C = Heat gained by A
msCΔTC=msAΔTA
sC(28θ)=sA(12θ)

Using (3), we get
16sA(28θ) = 15sA(θ12)
θ=20.26C

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