Two rods one of aluminum and the other of copper are joined

Two rods one of aluminum and the other of copper, are joined end to end. The cross-section area of each 4.0 times 10^-4 m^2, and the length of each is 0.040 m. The free end of the aluminum rod is kept at 302 degree C, while the free end of the copper rod is kept at 25 degree C. The loss of heat through the sides of the rods may be ignored, (a) What is the temperature at the aluminum copper interface? (b) How much heat is conducted through the unit in 2.0 s? (c) What is the temperature in the aluminum rod at a distance of 0.015 m from the hot end?

Solution

let the temperature at the junction be (on ^oCelsius scale)

the same heat current passes through aluminum and copper rods. Thus,

Q/t = K_Al * A * (302 - )/(0.04) = K_Cu * A * ( - 25)/(0.04)

=> K_Al * (302 - ) = K_Cu * ( -25)

=> 200 * (302 -) = 400 * ( - 25)

=> 302 - = 2 - 50

=> = 117.333^oC

heat flow per second => Q/t = K_Al * A * (302 - )/(0.04)

=> Q/t = 200 * 4 * 10^-4 * (302 - 117.333)/(0.04)

=> Q/t = 369.33 Joules/sec

Heat flow in 2 seconds = 369.33 * 2 = 738.66 Joules