A copper rod and a steel rod of equal cross -sections and lengths `(L)` are joined side by side and connected between two heat baths as shown in the figure. If heat flows through them from `x=0` to `x=2L` at a steady rate, and conductivities of the metals are `K_(cu)` & `K_("steel")(K_(cu)gtK_("steel"))`, then the temperature varies with `x` as (convention and radiation are negligible)

Three rodsP,Q and R having, samearea of cross section and lengths are connected with each other as shown in figure. The rod through which no heat will flow is (Thermal conductivities of rods P,Q,andR are 2k,4k and 2k respectively)

Two Aluminium rods and a steel rod of equal cross-sectional area and equal length l_(0) are joined rigidly side by side as shown in figure. Initially the rods are at 0^(@)C . Find the length of the rod at the temperature theta if young's modulus of elasticity of the aluminium and steel are Y_(a) and Y_(s) respectively and coefficient of linear expansion of aluminum and steel are alpha_(a) and alpha_(s) respectively. |{:("Aluminium"),("Steel"),("Aluminium"):}|

Find the rate of heat flow through a cross section of the rod shown in figure (theta_(2)gttheta_(1)) . Thermal conductivity of the material of the rod is K.

Find the rate of heat flow through a cross section of the rod shown in figure (theta_(2)gttheta_(1) . Thermal conductivity of the material of the rod is K.

Find the rate of heat flow through a cross section of the rod shown in figure (theta_(2)gttheta_(1)) . Thermal conductivity of the material of the rod is K.

Three rods each of length l and cross sectional area A joined in series between two heat reservoirs as shown in the figure. Their conductivities are 2K, K and (K)/(2) , respectively. Assuming that the conductors are insulated from surroundings, the temperatures T_(1) and T_(2) of the junctions in steadly state condition are respectively.

A rod of 1m length and area of cross-section 1cm^(2) is connected across two heat reservoirs at temperature 100^(@)C and 0^(@)C as shown. The heat flow per second through the rod in steady state will be [Thermal conductivity of material of rod =0.09kilocalm^(-1)s^(-1)('^(@)C) ]

Two steel rods and an aluminum rod of equal length l_0 and equal cross section are joined rigidly at their ends as shown in the figure below. All the rods are in a state of zero tension at 0^@C . Find the length of the system when the temperature is raised to theta . Coefficient of linear expansion of aluminum and steel are alpha_a and alpha_s respectively. Young's modulus of aluminum is Y_a and of steel is Y_s .