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Questions on calorimetry without phase change

Question

Equal masses of three liquids A, Band C have temperatures 10°C, 25°C and 40°C respectively.. If A and B are mixed, the mixture has a temperature of 15°C. If B and C are mixed, the mixture has a temperature of 30°C. If A and Care mixed, the mixture will have a temperature of:

Moderate

A

29°C
B

25°C
C

20°C
D

16°C

Solution

If A and B are mixed
$m \times s_{A} \times (15 - 10) = m \times s_{B} \times (25 - 15) \Rightarrow s_{A} = 2 s_{B}$
If B and C are mixed
$m \times s_{B} \times (30 - 25) = m \times s_{C} \times (40 - 30) \Rightarrow s_{C} = \frac{1}{2} s_{B}$
If A and C are mixed
$m \times (2 s_{B}) \times (θ - 10) = m \times (\frac{1}{2} s_{B}) \times (40 - θ) \Rightarrow θ = 16^{o} C$

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