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