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  4. A liquid of mass M and specific heat S is at a temperature 2t. If another liquid of mass M and thermal capacity 1.5 times, at a temperature of (t/3) is added to it, the resultant temperature will be :

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Q. A liquid of mass $M$ and specific heat $S$ is at a temperature $2t.$ If another liquid of mass $M$ and thermal capacity $1.5$ times, at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be :

NTA AbhyasNTA Abhyas 2020

Solution:

Let the common temperature of the mixture be $T$ .
For first liquid, mass, $M$ , specific heat of liquid, $S$ and initial temperature of liquid, $2t$ .
For second liquid, mass, $M$ , specific heat of liquid, $1.5S$ and initial temperature of liquid, $\frac{t}{3}$
Heat loss by the hot liquid $=$ Heat consumed by cold liquid
$MS\left(2 t - T\right)=M\left(1 . 5 S\right)\left(T - \frac{t}{3}\right)\Rightarrow 2t-T=1.5T-\frac{t}{2}\Rightarrow \frac{5}{2}T=\frac{5}{2}t$
$\Rightarrow T=t$