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

(2/3) T

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(8/5) T

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(3/5) T

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(3/2) T

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Solution

The correct option is D
(3/2) T

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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The correct option is D
(3/2) T

Temperature of mixture is given by

$T$ = $\frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2}}{m_{1} c_{1} + m_{2} c_{2}}$ = $\frac{m c 2 T + \frac{m}{2} 2 c T}{m c + \frac{m}{2} 2 c}$ = $\frac{3}{2} T$