Question 107 of 168
When of a liquid at is added to of a liquid at temperature , the temperature of the mixture becomes . The temperature of the mixture, if of liquid at is added to of liquid at , will be:
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Answer: (C)
Heat loss Heat gain
$\begin{array}{l}
\Rightarrow 100 \times \mathrm{S}_{\mathrm{A}} \times(100-90)=50 \times \mathrm{S}_{\mathrm{B}} \times(90-75) \\
2 \mathrm{~S}_{\mathrm{A}}=1.5 \mathrm{~S}_{\mathrm{B}} \Rightarrow \mathrm{S}_{\mathrm{A}}=\frac{3}{4} \mathrm{~S}_{\mathrm{B}}
\end{array}$
Now,
$\begin{array}{l}
300-3 \theta=2 \theta-100 \\
400=5 \theta \Rightarrow \theta=80^{\circ} \mathrm{C}
\end{array}$
$\begin{array}{l}
\Rightarrow 100 \times \mathrm{S}_{\mathrm{A}} \times(100-90)=50 \times \mathrm{S}_{\mathrm{B}} \times(90-75) \\
2 \mathrm{~S}_{\mathrm{A}}=1.5 \mathrm{~S}_{\mathrm{B}} \Rightarrow \mathrm{S}_{\mathrm{A}}=\frac{3}{4} \mathrm{~S}_{\mathrm{B}}
\end{array}$
Now,
$\begin{array}{l}
300-3 \theta=2 \theta-100 \\
400=5 \theta \Rightarrow \theta=80^{\circ} \mathrm{C}
\end{array}$