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Three liquids are at temperatures of 4 ◦C, 21◦C, and 31◦C, respectively. Equal masses of the...

Three liquids are at temperatures of 4 ◦C, 21◦C, and 31◦C, respectively. Equal masses of the first two liquids are mixed, and the equilibrium temperature is 6◦C. Equal masses of the second and third are then mixed, and the equilibrium temperature is 28◦C. Find the equilibrium temperature when equal masses of the first and third are mixed. Answer in units of ◦C.

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Answer #1

Initial temperature of the first liquid = T1 = 4 oC

Initial temperature of the second liquid = T2 = 21 oC

Initial temperature of the third liquid = T3 = 31 oC

Specific heat of the first liquid = C1

Specific heat of the second liquid = C2

Specific heat of the third liquid = C3

Equilibrium temperature when equal masses of first and second liquid are mixed = T4 = 6 oC

mC1(T4 - T1) = mC2(T2 - T4)

C1(6 - 4) = C2(21 - 6)

C1 = 7.5C2

Equilibrium temperature when equal masses of second and third liquid are mixed = T5 = 28 oC

mC2(T5 - T2) = mC3(T3 - T5)

C2(28 - 21) = C3(31 - 28)

C3 = 2.333C2

Equilibrium temperature when equal masses of first and third liquid are mixed = T6

mC1(T6 - T1) = mC3(T3 - T6)

C1(T6 - 4) = C3(31 - T6)

(7.5C2)(T6 -4) = (2.333C2)(31 - T6)

3.214(T6 - 4) = 31 - T6

3.214T6 - 12.856 = 31 - T6

4.214T6 = 43.856

T6 = 10.407 oC

Equilibrium temperature when equal masses of first and third liquid are mixed is 10.407 oC.

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