Three liquids with masses $m_{1}, m_{2}, m_{3}$ are thoroughly mixed. If their specific heats are $C_1, C_2, C_3$ and their temperatures $T_1, T_2, T_3$ respectively, then the temperature of the mixture is
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Let the final temperature be T °C.
Total heat supplied by the three liquids in coming down to 0°C = $m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$ ..... (i)
Total heat used by three liquids in raising temperature from 0 o C to T o C
= $m_{1} c_{1} T + m_{2} c_{2} T + m_{3} c_{3} T$ .....(ii)
By equating (i) and (ii) we get
$\left(m_{1}c_{1} + m_{2}c_{2} + m_{3}c_{3}\right)T$
= $m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$
⇒ ⇒ $T = \frac{m_1 c_1 T_1 + m_2 c_2 T_2 + m_3 c_3 T_3}{m_1 c_1 + m_2 c_2 + m_3 c_3}$ .
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