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.