The ends $Q$ and $R$ of two thin wires, $PQ$ and $RS$, are soldered (joined) together. Initially each of the wires has a length of $1\, m$ at $10^{\circ} C$. Now the end $P$ is maintained at $10^{\circ} C$, while the end $S$ is heated and maintained at $400^{\circ} C$. The system is thermally insulated from its surroundings. If the thermal conductivity of wire $PQ$ is twice that of the wire RS and the coefficient of linear thermal expansion of $PQ$ is $1.2 \times 10^{-5} K ^{-1}$, the change in length of the wire $PQ$ is