Home
Class 11
PHYSICS
Four identical rods AB, CD, CF and DE ar...

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature `T_(1)` , `T_(2)` and `T_(3)` respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

Text Solution

Verified by Experts

Let `T_(B)` be the temperature at B
AB = CD = DE = CF = L & CB = BD = `L/2`
`thereforeFCB=EDB=(3L)/2`
Heat flowing per second towards B from E via D is
`H_(1)=(KA(T_(2)-T_(B)))/((3L)/2)`
Heat flowing per second towards B from F via C is
`H_(2)=(KA(T_(3)-T_(B)))/((3L)/2)`
Heat flowing per second towards A from B is
`H_(3)=(KA(T_(B)-T_(1)))/(L)`
In steady state, `H_(1)+H_(2)=H_(3)`
`(KA(T_(2)-T_(B)))/((3L//2))+(KA(T_(3)-T_(B)))/((3L//2))=(KA(T_(B)-T_(1)))/(L)`
on solving we get `rArrT_(B)=(2T_(2)+2T_(3)+3T_(1))/7`
Promotional Banner

Similar Questions

Explore conceptually related problems

Eleven identical rods are arranged as shown in Fig. Each rod has length l , cross sectional area A and thermal conductivity of material k. Ends A and F are maintained at temperatures T_1 and T_2(ltT_1) , respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer ((dQ)/(dt)) in each rod is

Four thin identical rods AB, AC, BD and EF made of the same material are joined as shown. The free-ends C,D and F are maintained at temperature T_(1),T_(2) and T_(3) respectively. Assuming that there is no loss of heat of the surroundings, the temperature at joint E when the steady state is attained is (1)/(K) (2T_(1)+2T_(2)+3T_(3)) . Find K (E is mid point of AB)

All the rods have same conductance 'K' and same area of cross section ' A' . If ends A and C are maintained at temperature 2T_(0) and T_(0) respectively then which of the following is // are correct?

Five rods of same material and same cross-section are joined as shown. Lengths of rods ab, ad and bc are l, 2l and 3l respectively. Ends a and c are maintained at temperatures 200^(@)C and 0^(@)C respectivelly. For what length x of rod dc there will be no heat flow through rod bd ?

A composite rod made of three rods of equal length and cross-section as shown in fig. The thermal conductivites of the materials of the rods are K//2 , 5K and K respectively. The end A and end B are at constant tempertures. All heat entering the face A goes out of the end B there being no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is

Three rods AB, BC and BD having thermal conductivities in the ratio 1:2:3 and lengths in the ratio 2:1:1 are joined as shown in Fig. The ends A, C and D are at temperature T_1 , T_2 and T_3 respectively Find the temperature of the junction B. Assume steady state.

A circular ring (centre O) of radius a, and of uniform cross section is made up of three different metallic rods AB, BC and CA (joined together at the points A, B and C in pairs) of thermal conductivityies alpha_1 , alpha_2 and alpha_3 respectively (see diagram). The junction A, B and C are maintained at the temperatures 100^@C , 50^@C and 0^@C , respectively. All the rods are of equal lengths and cross sections. Under steady state conditions, assume that no heat is lost from the sides of the rods. Let Q_1 , Q_2 and Q_3 be the rates of transmission of heat along the three rods AB, BC and CA. Then

A circular ring (centre O) of radius a, and of uniform cross section is made up of three different metallic rods AB, BC and CA (joined together at the points A, B and C in pairs) of thermal conductivityies alpha_1 , alpha_2 and alpha_3 respectively (see diagram). The junction A, B and C are maintained at the temperatures 100^@C , 50^@C and 0^@C , respectively. All the rods are of equal lengths and cross sections. Under steady state conditions, assume that no heat is lost from the sides of the rods. Let Q_1 , Q_2 and Q_3 be the rates of transmission of heat along the three rods AB, BC and CA. Then

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 conductivities 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 temperature T_(2) .

A rod of length l and cross-section area A has a variable thermal conductivity given by K = alpha T, where alpha is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperature T_(1) and T_(2) (T_(1)gtT_(2)) . Heat current flowing through the rod will be