question_answer

Two rectangular blocks A and B of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of A is 100°C and that of B at the other end is 0°C. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be           [MP PMT 1985]

A)            25°C                                         

B)            50°C

C)            75°C                                         

D)                 100°C

Correct Answer: A

Solution :

                   It is given that \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{1}{3}\] Þ \[{{K}_{1}}=K\] then \[{{K}_{2}}=3K\] the temperature of the junction in contact \[\theta =\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]\[=\frac{1\times 100+3\times 0}{1+3}=\frac{100}{4}\]= 25°C