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 isA- c1 T1-c2 T2-c3 T3-m1 c1-m2 c2-m3 c3B- m1 c1-m2 c2-m3 c3-m1 c1-m2 c2-m3 c3m1 c1-m2 c2-m3 c3C- m1 c1 T1-m2 c2 T2-m3 c3 T3-m1 T1-m2 T2-m3 T3D- m1 T1-m2 T2-m3 T3-c1 T1-c2 T2-c3 T3

The correct option is B Let the final temperature be T^∘ C. Total heat supplied by the three liquids in coming down to 0^∘ C = m_1c_1T_1 + m_2c_2T_2 + m_3c_3T ...

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Standard VIII

Physics

Specific Heat

Three liquids...

Question

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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Solution

The correct option is B
Let the final temperature be $T^{\circ} C .$
Total heat supplied by the three liquids in coming down to $0^{\circ} C = m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3} . . . . . . (i)$
Total heat used by three liquids in raising temperature from $0^{\circ} C t o T^{\circ} C = m_{1} c_{1} T + m_{2} c_{2} T + m_{2} c_{2} T + m_{3} c_{3} T . . . . . (i i)$
By equating (i) and (ii) we get $(m_{1} c_{1} + m_{2} c_{2} + m_{2} c_{2} + m_{3} c_{3}) T = m_{1} c_{1} T 1 + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3} \Rightarrow T = \frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}}{m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}}$

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