To measure thermal conductivity, two similar $1-$cm$-$thick specimens are placed in an apparatus shown in the accompanying sketch. Electric current is supplied to the $6-$cm by $6-$cm guarded heater, and a wattmeter shows that the power dissipation is $10$ watts$($W$).$ Thermocouples attatched to the warmer and to the cooler surfaces show tempuratures of $322$ and $300$K$,$ respectively. Calculate the thermal conductivity of the material at the mean tempurature in W$/($m K$).$