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-A- c1 T1-c2 T2-c3 T3-m1 c1-m2 c2-m3 c3B- m1 c1 T1-m2 c2 T2-m3 c3 T3-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

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

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Solution

The correct option is B
Given, $T_{1}, T_{2} a n d T_{3}$ are the temperature of liquids with mass $m_{1}, m_{2} a n d m_{3}$ with specific heats $c_{1}, c_{2} a n d c_{3}$
Let the final temperature be $T^{\circ} C$ .
Total heat supplied by the three liquids in coming down to $0^{\circ} C$ is
$m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$ ......(i)

Total heat used by three liquids in raising temperature from $0^{\circ} C to T^{\circ} C$ is
$m_{1} c_{1} T + m_{2} c_{2} T + m_{3} c_{3} T$ .....(ii)
By equating (i) and (ii) we get,
$m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}) T = m_{1} c_{1} T 1 + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$
or, $T = \frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}}{m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}}$

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Three liquids with masses m1,m2,m3 are thoroughly mixed. If their specific heats are c1,c2,c3 and their temperatures are T1,T2,T3 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: