Two slabs of thickness `x_1 and x_2` and thermal conductivities `k_1 and k_2` are in thermal contact with each other as shown in Fig. 11.4. The temperature of their outer surfaces are `T_1 and T_2` respectively. `(T_1 gt T_2)`. Find the temperature at the surface.
Text Solution
Verified by Experts
Let T be the temperature of the interface. The rate of flow of heat through both the material will be same at the steady state. The area of cross-section of both the slabs is the same. Quantity of heat flowing per second through the two slabs is, `Q= ( k_1 A ( T_1 - T) )/( x_1 ) = (k_2 A (T- T_2 ) )/( x_2)` `(k_1 T_1 )/( x_1) - (k_1 T)/( x_1 ) = (k_2 T)/( x_2) - (k_2 T_2)/( x_2)` `((k_2)/( x_2) + (k_1)/( x_1) ) T = (k_1 T_1)/( x_1 ) + ( k_2 T_2 )/( x_2) , T = ((k_1 T_1)/( x_1 ) + (k_2 T_2)/(x_2) )/((k_1)/( x_1) + (k_2)/( x_2))` `((k_2 x_1 + k_1 x_2))/( x_1 x_2) T = (k_1 x_2 T_2 + k_2 x_1 T_2 )/( x_1 x_2)` `T= (k_1 x_2 T_1 + k_2 x_1 T_2)/( k_2 x_1 + k_1 x_2)`
Topper's Solved these Questions
THERMAL CONDUCTION
ICSE|Exercise CONCEPTUAL SHORT ANSWER QUESTIONS WITH ANSWERS|8 Videos
Two walls of thickness d_(1) and d_(2) and thermal conductivites K_(1) and K_(2) are in contact. In the steady state, if the temperature at the outer surfaces are T_(1) and T_(2) the temperature at the common wall is
Two plates eachb of area A, thickness L_1 and L_2 thermal conductivities K_1 and K_2 respectively are joined to form a single plate of thickness (L_1+L_2) . If the temperatures of the free surfaces are T_1 and T_2 . Calculate. (a) rate of flow of heat (b) temperature of interface and (c) equivalent thermal conductivity.
Two materials having coefficients of thermal conductivity '3k' and 'k' and thickness 'd' and '3d' respectively, are joined to form a slab as shown in the figures. The temperatures of the outer surfaces are theta_(2) and theta_(1) respectively (theta_(2) gt theta_(2)) . The temperature at the interface 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.
Two bars of same length and same cross-sectional area but of different thermal conductivites K_(1) and K_(2) are joined end to end as shown in the figure. One end of the compound bar it is at temperature T_(1) and the opposite end at temperature T_(2) (where T_(1) gt T_(2) ). The temperature of the junction is
Two rods of length l_(1) and l_(2) and coefficients of thermal conductivities k_(1) and K_(2) are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is
Two bodies of masses m_(1) and m_(2) and specific heat capacities S_(1) and S_(2) are connected by a rod of length l , cross-section area A , thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t=0 , the temperature of the first body is T_(1) and the temperature of the second body is T_(2)(T_(2)gtT_(1)) . Find the temperature difference between the two bodies at time t .
Two bodies of masses m_(1) and m_(2) and specific heat capacities S_(1) and S_(2) are connected by a rod of length l, cross-section area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t=0 , the temperature of the first body is T_(1) and the temperature of the second body is T_(2)(T_(2)gtT_(1)) . Find the temperature difference between the two bodies at time t.
The plots of intensity versus wavelength for three black bodies at temperature T_1,T_2 and T_3 respectively are as shown. Their temperatures are such that
Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T_(1) = 300K and T_(2) = 100 K , as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K_(1) and K_(2) respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K_(1)//K_(2)= __________.
ICSE-THERMAL CONDUCTION-SELECTED PROBLEMS (Taken from the Previous Years ISC, AISSCE, HSSCE various States. Boards Roorke Qns & NCERT text) FROM EXPERIMENT TO DETERMINE K
