A rod of length $L$ with sides fully insulated is of a material whose thermal conductivity varies with $\alpha$ temperature as $ K= \frac{\alpha }{T}$, where $\alpha$ is a constant. The ends of the rod are kept at temperature $T_1$ and $T_2$. The temperature $T$ at $x,$ where $x$ is the distance from the end whose temperature is $T_1$ is
A rod of length $L$ with sides fully insulated is of a material whose thermal conductivity varies with $\alpha$ temperature as $ K= \frac{\alpha }{T}$, where $\alpha$ is a constant. The ends of the rod are kept at temperature $T_1$ and $T_2$. The temperature $T$ at $x,$ where $x$ is the distance from the end whose temperature is $T_1$ is
- A
${T_1}{\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^{\frac{x}{L}}}$
- B
$\frac{x}{L}\ln \frac{{{T_2}}}{{{T_1}}}$
- C
${T_1}{e^{\frac{{{T_2}x}}{{{T_1}L}}}}$
- D
${T_1} + \frac{{{T_2} - {T_1}}}{L}x$
Similar Questions
Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$
Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$
- [IIT 2001]
What is thermal steady state ?
What is thermal steady state ?
The temperature of hot and cold end of a $20cm$ long rod in thermal steady state are at ${100^o}C$ and ${20^o}C$ respectively. Temperature at the centre of the rod is...... $^oC$
The temperature of hot and cold end of a $20cm$ long rod in thermal steady state are at ${100^o}C$ and ${20^o}C$ respectively. Temperature at the centre of the rod is...... $^oC$
Two rods $A$ and $B$ of different materials are welded together as shown in figure.Their thermal conductivities are $K_1$ and $K_2$ The thermal conductivity of the composite rod will be
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- [NEET 2017]
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is