The temperature $(T)$ of two samples of the same substance with masses $m_{1}$ and $m_{2}$ and temperatures $T_{1}$ and $T_{2}$ , when added together is _____.

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

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

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m_{1} T_{1} + m_{2} T_{2}

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m_{1} T_{2} + m_{2} T_{1}

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Solution

The correct option is B $\frac{m_{1} T_{1} + m_{2} T_{2}}{m_{1} + m_{2}}$
Let the specific heat of the substance be $S$ .
Heat released by one part of substance is absorbed by other part of substance to attain equilibrium temperature $T$ .
Total mass of substance, $M = m_{1} + m_{2}$
Thus $m_{1} S T_{1} + m_{2} S T_{2} = M S T$
$∴$ $m_{1} S T_{1} + m_{2} S T_{2} = (m_{1} + m_{2}) S T$

$⟹$ $T = \frac{m_{1} T_{1} + m_{2} T_{2}}{m_{1} + m_{2}}$

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