Question

 A copper rod and an aluminium rod of the same length and cross-sectional area are attached end to end. The copper end is placed in a furnace maintained at a constant temperature of 272°C. The aluminium end is placed in an ice bath held at a constant temperature of 0.00°C.

Calculate the temperature at the point where the two rods are joined. 

Answer 1

Solution.

$l_a=l_c;$

$S_a=S_c;$

$T_a=0^oC;$

$T_c=272^oC;$

$c_a=920J/kgK;$

$c_c=380J/kgK;$

$\rho_a=2700kg/m^3;$

$\rho_c=8900kg/m^3;$

$c_c\rho_c\Delta T_c=c_a\rho_a\Delta T_a;$

$\dfrac{\Delta T_c}{\Delta T_a}=\dfrac{c_a\rho_a}{c_c\rho_c};$

$\dfrac{T_c}{T_a}=\dfrac{920\sdot2700}{380\sdot8900}=0.7344;$

$\dfrac{T_c-T}{T-T_a}=0.7344;$

$T_c-T=0.7344T-0.7344T_a;$

$1.7344T=272;$

$T=157^oC;$

Answer: $157^oC.$