Question

Equal masses of three liquids A, B and 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 C are mixed, the mixture will have a temperature of 

(a) 16°C 

(b) 20°C 

(c) 25°C 

(d) 29°C

Answer 1

Correct Answer is: (a) 16°C 

θ = Σmsθ/Σms = m₁s₁θ₁ + m₂s₂θ₂ + / m₁s₁ + m₂s₂ +

For systems of equal mass, θ = Σmsθ/Σs

Let s₁, s₂ and s₃ be the specific heat capacities of A, B and C respectively.

For A + B, 15 = 10s₁ + 25s₂/s₁ + s₂  

or 5s₁ = 10s₂

or s₁ = 2s₂

For B + C, 30 = 25s₂ + 40s₃/s₂ + s₃

or 5s₂ = 10s₃ 

or s₃ = 0.5s₂.

For A + C, θ = 10s₁ + 40s₃/s₁ + s₃ = 10(2s₂) + 40(0.5)s₂/2s₂ +0.5s₂ = 40/2.5 =16.