Question

Four identical rods which have thermally insulated lateral surfaces are joined at point A. Points B,C,D & E are connected to large reservoirs. If heat flows into the junction from point B at rate of $1W$ and from point ‘C’ at $3W$ inside, flows out from D at $5W$, which relation (s) is//are correct for temperature of these points ?

(A) ${T_A} < {T_E}$
(B) ${T_B} = {T_C}$
(C) ${T_C} > {T_D}$
(D) ${T_B} = {T_E}$

Answer 1

Hint: In order to solve this question, we will first equate the total rate of heat flowing into point A and the total rate of heat flowing out of point B and then we will check each option for temperature relations at every four points.

Complete answer:
Let us assume the rate of heat flow through the rod EA be $xW$ into the point A and draw the rough diagram to represent the heat flow direction at each rod as

Now, total heat flowing into the point A is $(1 + 3 + x)W$ and the net flow of heat out of the point A is $5W$ now, equate both values we get,
$
  1 + 3 + x = 5 \\
  x = 1W \\
 $

Now, since heat is flowing from point E to A which means
$
  {T_E} > {T_A} \\
   \Rightarrow {T_A} < {T_E} \\
 $
So, option (A) is correct

Since, heat is flowing out of the point A to D but going into the point A from C which means
$
  {T_C} > {T_A} > {T_D} \\
   \Rightarrow {T_C} > {T_D} \\
 $
So, option (C) is correct.

Since rate of heat flow is equal in rods BA and EA so, we have
$
  {T_B} - {T_A} = {T_E} - {T_A} \\
  {T_B} = {T_E} \\
 $
So, option D is also correct.
But, ${T_B} \ne {T_C}$ so option (B) is incorrect.

Hence, the correct options are (A), (C), and (D)

Note:It should be remembered that, heat energy always flows from higher temperature point to the lower temperature point and for a closed system net heat flowing into the junction point is always equals to the net heat flowing out of the junction point.