A brass rod with thermal conductivity k=120W/m⋅K, cross-sectional area 3.0×10−4m2, and length 0.40m connects a heat reservoir at 200∘C to a 0.50kg aluminum block initially at 20∘C. Assume the temperature at the rod–block junction always equals the block’s temperature and that all energy conducted through the rod raises the block’s temperature. What is the block’s initial rate of temperature increase (dtdT) at the moment its temperature is 20∘C? (Specific heat of aluminum: c=900J/kg⋅K.)
a) 1.4×10−2K/s
b) 3.6×10−2K/s
c) 7.2×10−2K/s
d) 3.6×10−3K/s