A hot reservoir at 50oC is connected to a cold reservoir at -60oC by a cylindrical, thermal conductor. The thermal conductor has a constant radius of 5 cm, but is made up of two different metals. The first portion of the conductor, made of aluminum, is 8 cm long and has a thermal conductivity of 205 W/mK and is in contact with the hot reservoir. The second portion of the conductor, made of brass, is 10 cm long and has a thermal conductivity of 109 W/mK, and is in contact with the cold reservoir.
(a) What is the temperature at the junction between the aluminum and brass?
(b) What is the rate at which heat is passing through the conductor?