The temperatures of equal masses of three different liquids A , B and C are 12 degree celcius , 19degree - Physics - Thermodynamics

Question

The temperatures of equal masses of three different liquids A ,
B and C are 12 degree celcius , 19degree celcius and 28degree
celcius respectively The temperature when A and B are mixed , is
16degree celcius andwhen B and C are mixed , is 23 degree celcius
What will be the temperature when A and C are mixed ?

Himanshu · Accepted Answer

Let a, b and c be the specific heat capacities of liquids A, B and C.

Let the mass of the liquids be m.

When A and B are mixed:

$m a (16 - 12) = m b (19 - 16) \Rightarrow 4 a = 3 b$

When B and C are mixed:

$m b (23 - 19) = m c (28 - 23) \Rightarrow 4 b = 5 c$

Therefore, 16a = 12b = 15c

Let x be the temperature when A and C are mixed

$m a (x - 12) = m c (28 - x) \Rightarrow \frac{a}{c} = \frac{15}{16} = \frac{28 - x}{x - 12} \Rightarrow 15 x - 180 = 448 - 16 x \Rightarrow 31 x = 628 \Rightarrow x = 20.25 \deg$