A composite bar of uniform cross-section is made of 25 cm of copper, 10 cm of nickel and 15 cm of aluminium with perfect thermal contacts. The free copper end of the rod is at `100^(@)C` and the free aluminium ends is at `0^(@)C`. If `K_(Cu)=2K_(Al)" and "K_(Al)=3K_(Ni)`, then the temperatures of Cu-Ni and Ni-Al junctions are respectively.
(Assume no loss of heat occurs from the sides of the rod, K-thermal conductivity).

Options

A. `82.3" "^(@)C, 31.3" "^(@)C`
B. `78.3" "^(@)C, 26.1" "^(@)C`
C. `70" "^(@)C, 23.3" "^(@)C`
D. `90.3" "^(@)C, 30.1" "^(@)C`

Answer

B

Explanation

Heat transfer, `(DeltaQ)/(Deltat)=(KA(T_(1)-T_(2)))/L`
or `(K_(Cu)(A)(100-T_(1)))/25=(K_(Ni)(A)(T_(1)-T_(2)))/10=(K_(Al)(A)(T_(2)))/15`
`because " "K_(Cu)=2K_(Al) " and "K_(Al)=3K_(Ni)`
`therefore " "(2K_(Al)(A)(100-T_(1)))/25=(K_(Al)(A)(T_(2)))/15`
`rArr " "6T_(1)+5T_(2)=600 " ...(i)"`
`rArr " "(K_(Ni)(A)(T_(1)-T_(2)))/10=(3K_(Ni)(A)(T_(2)))/15`
`rArr " "T_(1)=3T_(2) " ...(iii)"`
From Eqs. (i) and (ii), we get
`" "T_(2)=26.08^(@)C`
` " "T_(1)=78.26^(@)C`
Hence, the temperature of Cu-Ni and Ni-Al junctions are respectively, `78.26^(@) " and "26.08^(@)C`.