Seven rods A, B, C, D, E, F and G are joined as shown in figure. All the rods have equal cross-sectional area A and length l. The thermal conductivies of the rods are `K_(A)=K_(C)=K_(0), `K_(B)=K_(D)=2K_(0), `K_(E)=3K_(0), `K_(F)=4K_(0)` and `K_(G)=5K_(0)` . The rod E is kept at a constant temperature `T_(1)` and the rod G is kept at a constant temperature `T_(2)(T_(2)gtT_(1))` . (a) Show that the rod F has a uniform temperature `T=(T_(1)+2T_(2))//3` . (b) Find the rate of heat flowing from the source which maintains the tempeature `T_(2)` .

Answer

A, B, C, D

Explanation

The temperature at the both ends of bar F is same
Rate of heat flow to right =rate of heat flow to left
`implies(Q/T)_A +(Q/T)_C=(Q/T)_B+(Q/T)_D`
`(K_A a(T-T_1))/l +(K_C a(T-T_1))/2l`
` =(K_B a(T_2-T))/l+(K_D a(T_2-T))/2l`
`implies2K_0(T-T_1)=2xx2k_0(T_2-T)`
`impliesT-T_1=2(T_2-T)`
`3T=2T_2+T_1`
`T=(T_1+2T_2)/3`.