Two bars of thermal conductivities K and 3K and lengths \[1cm\] and \[2cm\] respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is \[{{0}^{o}}C\] and \[{{K}^{2}}/l\] respectively (see figure), then the temperature \[\varphi \]of the interface is

• A. \[{{50}^{o}}C\]
• B. \[\frac{100}{3}{{\ }^{o}}C\]
• C. \[{{60}^{o}}C\]
• D. \[\frac{200}{3}{{\ }^{o}}C\]