Question

Two liquids A and B are at temperatures of 75°C and 15°C respectively. Their masses are in the ratio 2:3 and their specific heat are in the ratio 3:4 . The resultant temperature of the mixture if the liquids A and B mixed ... is
(A) 35°C (B) 75°C (C) 80°C (D) none

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Answer 1

Given,

The temperature of liquid A = 75°

The temperature of liquid B = 15°

The ratio of masses, A: B = 2:3

The ratio of specific heats,  A: B = 3:4

To Find,

The resultant temperature when A and B are mixed.

Solution,

Let the masses of A and B be 2$x$ and 3$x$ respectively.

Let the specific heats of A and B be 3$y$ and 4$y$ respectively.

Heat lost = Heat gained

The formula to calculate heat, $Q = ms$Δ$T$

In this case, liquid A loses heat and liquid B gains heat.

∴ $m_{A}s_{A} (T_{initial} - T_{final}) = m_{B }s_{B} (T_{final} - T_{initial})$

⇒$(2x)(3y)(75-T_{final}) = (3x)(4y)(T_{final}-15)$

⇒$75-T_{final} = 2(T_{final} -15)$

⇒$3T_{final} = 105\\T_{final} = 35$

Henceforth, the final temperature of the mixture is 35°C.