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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?


A

30.26°C

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B

40.26°C

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C

20.26°C

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D

10.26°C

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Solution

The correct option is C

20.26°C


Let m = mass of each liquid, when A and B are mixed,

Heat lost by B = Heat gained by A

msB (19 - 16) = msA (16 - 12) 3 sB = 4SA . . . .(1)

When B and C are mixed, Heat lost by C = Heat gained by B

msC (28 - 23) = msB (23 - 19) 5sC = 4SB . . . .(2)

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

When A and C are mixed, Let θ = final temperature

Heat lost by C = heat gained by A

msC (28θ) = msB (θ12)

Using (3), we get

15sC(28θ) = 15sA(θ12) 16sA (28θ) = 15sA(θ12)

On solving for θ, we get θ = 16 × 28 + 12 × 1516+15 θ = 20.26C


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