Question

Three rods made of the same materail and having same cross-section area but diferent length 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction is

A. `10.8^(@)C`
B. `14.6^(@)C`
C. `16.4^(@)C`
D. `18.2^(@)C`

Answer 1

Correct Answer - C
Let `theta` be the temperature of junction and `H_(1), H_(2) and H_(3)` the heat currents. Then

` H_(1) = H-(2)=H_(3)`
or `(30-theta)/((30/(KA))) = (theta-20)/((20/(KA))) + (theta-10)/((30/(KA)))`
or `2(30-theta)= 3(theta-20)+ 3(2theta-20)`
or `theta = 16.36^(@)C~~ 16.4^(@)C`