As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates…

As per the given figure, two plates A and B of thermal conductivity K and $\displaystyle 2$ K are joined together to form a compound plate. The thickness of plates are $\displaystyle 4.0$ cm and $\displaystyle 2.5$ cm respectively and the area of cross-section is $\displaystyle 120 \mathrm{~cm}^2$ for each plate. The equivalent thermal conductivity of the compound plate is $\displaystyle \left(1+\frac{5}{\alpha}\right) \mathrm{K}$, then the value of $\displaystyle \alpha$ will be \_\_\_\_.