Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to
Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to
- [IIT 1995]
- A
$\frac{1}{{(\sqrt 2 + 1)}}$
- B
$\frac{3}{{(\sqrt 2 + 1)}}$
- C
$\frac{1}{{2(\sqrt 2 - 1)}}$
- D
$\frac{1}{{\sqrt 3 (\sqrt 2 - 1)}}$
Similar Questions
A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ........... $Wm^{-2}$
A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ........... $Wm^{-2}$
- [JEE MAIN 2019]
A composite block is made of slabs $A, B, C, D$ and $E$ of different thermal conductivities (given in terms of a constant $K$ ) and sizes (given in terms of length, $L$ ) as shown in the figure. All slabs are of same width. Heat $'Q'$ flows only from left to right through the blocks. Then in steady state $Image$
$(A)$ heat flow through $A$ and $E$ slabs are same.
$(B)$ heat flow through slab $E$ is maximum.
$(C)$ temperature difference across slab $E$ is smallest.
$(D)$ heat flow through $C =$ heat flow through $B +$ heat flow through $D$.
A composite block is made of slabs $A, B, C, D$ and $E$ of different thermal conductivities (given in terms of a constant $K$ ) and sizes (given in terms of length, $L$ ) as shown in the figure. All slabs are of same width. Heat $'Q'$ flows only from left to right through the blocks. Then in steady state $Image$
$(A)$ heat flow through $A$ and $E$ slabs are same.
$(B)$ heat flow through slab $E$ is maximum.
$(C)$ temperature difference across slab $E$ is smallest.
$(D)$ heat flow through $C =$ heat flow through $B +$ heat flow through $D$.
- [IIT 2011]
Heat current is maximum in which of the following (rods are of identical dimension)
Heat current is maximum in which of the following (rods are of identical dimension)
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