A Heat-Conducting Rod That Is Wrapped in Insulation Is Constructed $m ^ { 2 }$

A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 $m ^ { 2 }$ The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A . The end of the rod in alloy A is maintained at a temperature of $10 ^ { \circ } \mathrm { C }$ and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be $40 ^ { \circ } \mathrm { C }$ and the rate of heat flow in the rod is measured at 56 W. What is the thermal conductivity of alloy A?

A) $130 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
B) $140 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
C) $120 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
D) $135 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$
E) $125 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$