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

\frac{c_{1} T_{1} + c_{2} T_{2} + c_{3} T_{3}}{m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}}

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\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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\frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}}{m_{1} T_{1} + m_{2} T_{2} + m_{3} T_{3}}

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\frac{m_{1} T_{1} + m_{2} T_{2} + m_{3} T_{3}}{c_{1} T_{1} + c_{2} T_{2} + c_{3} T_{3}}

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Solution

The correct option is B $\frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}}{m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}}$
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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Q. 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

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 are $T_{1}, T_{2}, T_{3}$ respectively, then the temperature of the mixture is:

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