A liquid of mass $m$ and specific heat $c$ is heated to a temperature $2 T$ . Another liquid of mass $m / 2$ and specific heat $2 c$ is heated to a temperature $T$ . If these two liquids are mixed, the resulting temperature of the mixture is

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Solution

The correct option is D
Total heat supplied by the two liquids ( $T_{2} t o 0^{\circ}$ )

$m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2}$

Total heat used by two liquids in raising temperature to $T$ to $0^{\circ}$

$m_{1} c_{1} T + m_{2} c_{2} T$

By equating the above two we get

$m_{1} c_{1} T + m_{2} c_{2} T$ = $m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2}$

Temperature of mixture is given by $T = \frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2}}{m_{1} c_{1} + m_{2} c_{2}} = \frac{m . c .2 T + \frac{m}{2} .2 . c . T}{m . c . + \frac{m}{2} .2 c} = \frac{3}{2} T$

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