The time taken for a calorimeter containing 75   g of water at 62 ° C to cool to 58 ° C is 9…

The equation of water equivalent in the first case is,

$$\begin{gathered} mc\frac{dT}{dt}=-k\left[\frac{\left(T_1+T_2\right)}{2}-T_0\right] \\ \Rightarrow \left(75+x\right)c\frac{\left(62-58\right)}{9}=-k\left[\frac{\left(62+58\right)}{2}-T_0\right]....\left(1\right) \end{gathered}$$

is the second case the equation of water equivalent,

$\Rightarrow \left(105+x\right)c\frac{\left(62-58\right)}{12}=-k\left[\frac{\left(62+58\right)}{2}-T_0\right]...\left(2\right)$

$$\begin{gathered} \frac{\left(75+x\right)}{9}=\frac{{\displaystyle \left(75+x\right)}}{12} \\ \Rightarrow x=15 \mathrm{g} \end{gathered}$$