Question

Metal rods X and Y of identical cross-sectional area, have lengths 60 cm and 30 cm respectively. They are made of metals of thermal conductivities l_X and l_Y. They are well-lagged and joined end - to - end as shown in the diagram. One end of X is maintained at 100ŗC and the opposite end of Y is maintained at 0ŗC. When steady conditions have been reached, the temperature of the junction is found to be 25⁰C.What is the value of $\frac{\lambda_{X}}{\lambda_{Y}}$ ?

• A. 1/6
• B. 2/3
• C. 25/24
• D. 3/2

Answer 1

Answer: (B)

2/3

Answer 2

$\frac { \lambda _ { \mathrm { X } } \mathrm { A } ( 100 - 25 ) } { 60 } = \frac { \lambda _ { \mathrm { Y } } \mathrm { A } ( 25 - 0 ) } { 30 }$ $\frac{\lambda_{X}}{\lambda_{Y}}$= $\frac{25 \times 60}{30 \times 75}$ = $\frac{2}{3}$