A solid steel rod of length 0.50m and cross-sectional area 1.5×10−4m2 has one end maintained at 200∘C. The other end is pressed firmly against a 0.20kg aluminum cube that is initially at 20∘C. The lateral surface of the rod is perfectly insulated, and the cube is surrounded by an insulating jacket on all sides except the face that contacts the rod. Neglect any energy exchange with the surrounding air.
Useful data:
• Steel: thermal conductivity ksteel=50W⋅m−1⋅K−1
• Aluminum: specific heat cAl=900J⋅kg−1⋅K−1
(a) Calculate the initial rate at which thermal energy is transferred through the rod to the cube.
(b) Determine the initial rate of temperature increase of the aluminum cube.
(c) Assuming the energy transfer rate found in part (a) remains constant until the cube reaches 50∘C, calculate the time required for the cube to reach that temperature.