Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are ${K_1}\,\,{\rm{and}}\,\,{K_2}$. The temperature of the free ends of the first and second rods are maintained at ${\theta _1}\,\,{\rm{and }}{\theta _2}$ respectively. The temperature of the common junction is
Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are ${K_1}\,\,{\rm{and}}\,\,{K_2}$. The temperature of the free ends of the first and second rods are maintained at ${\theta _1}\,\,{\rm{and }}{\theta _2}$ respectively. The temperature of the common junction is
- A
$\frac{{{\theta _1} + {\theta _2}}}{2}$
- B
$\frac{{{K_2}{K_2}}}{{{K_1} + {K_2}}}({\theta _1} + {\theta _2})$
- C
$\frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$
- D
$\frac{{{K_2}{\theta _1} + {K_1}{\theta _2}}}{{{K_1} + {K_2}}}$
Similar Questions
On heating one end of a rod, the temperature of whole rod will be uniform when
On heating one end of a rod, the temperature of whole rod will be uniform when
$A$ cylinder of radius $R$ made of a material of thermal conductivity ${K_1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity ${K_2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
$A$ cylinder of radius $R$ made of a material of thermal conductivity ${K_1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity ${K_2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
- [IIT 1988]
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} - {T_1})K}}{x}} \right)f$, with $f $ which equal to
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} - {T_1})K}}{x}} \right)f$, with $f $ which equal to
- [AIIMS 2017]
$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium
$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium
Woollen clothes are used in winter season because woolen clothes
Woollen clothes are used in winter season because woolen clothes
- [AIIMS 1998]