A substance of mass $m_{1}$ with specific heat capacity $s_{1}$ and initial temperature $θ_{1}$ is mixed with another substance of mass $m_{2}$ , specific heat capacity $s_{2}$ and initial temperature $θ_{2}$ respectively. Then, their equilibrium temperature is ........(take $θ_{1} > θ_{2}$ )

\frac{m_{1} s_{1} θ_{1} - m_{2} s_{2} θ_{2}}{m_{1} s_{1} - m_{2} s_{2}}

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\frac{m_{1} s_{1} θ_{1} - m_{2} s_{2} θ_{2}}{m_{1} s_{1} + m_{2} s_{2}}

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\frac{m_{2} s_{2} θ_{2} - m_{1} s_{1} θ_{1}}{m_{1} + m_{2}}

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\frac{m_{1} s_{1} θ_{1} + m_{2} s_{2} θ_{2}}{m_{1} s_{1} + m_{2} s_{2}}

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Solution

The correct option is D $\frac{m_{1} s_{1} θ_{1} + m_{2} s_{2} θ_{2}}{m_{1} s_{1} + m_{2} s_{2}}$
Let the final temperature be $θ$
$θ_{1} > θ_{2}$
$m_{1} S_{1} (θ_{1} - θ) = m_{2} S_{2} (θ - θ_{2}) \Rightarrow m_{1} S_{1} θ_{1} - m_{1} S_{1} θ = m_{2} S_{2} θ - m_{2} S_{2} θ_{2} \Rightarrow m_{1} S_{1} θ + m_{2} S_{2} θ = m_{1} S_{1} θ_{1} + m_{2} S_{2} θ_{2} \Rightarrow θ = \frac{m_{1} S_{1} θ_{1} + m_{2} S_{2} θ_{2}}{m_{1} S_{1} + m_{2} S_{2}}$

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