Question

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Figure 1). The copper end is placed in a furnace maintained at a constant temperature TCu = 230 ∘C . The aluminum end is placed in an ice bath held at a constant temperature of 0.0∘C. Calculate the temperature at the point where the two rods are joined.

Answer 1

K = thermal conductivity

KCu = 385 J/s/m-^oC

Kal = 205 J/s/m-^oC

Conduction = dE/dt

P = k*A*dt/L

in given situation

P_Al = P_Cu

P_Al = P_Cu

k_Al*A_Al*dt_Al/L_Al = k_Cu*A_Cu*dt_Cu/L_Cu

L & A be Same

k_Al*A*dt_Al/L = k_Cu*A*dt_Cu/L

k_Al*dt_Al = k_Cu*dt_Cu

k_Al*(T - T_c) = k_Cu*(T- T_h)

k_Al*(T - 0) = k_Cu*(T- T_h)

k_Al*T= k_Cu*T- k_Cu*T_h)

T = K_Cu*T_h/(K_Al­*K_Cu)

T = 385*230/(385+205)

T = 150^o C