Question 476: Thermodynamics & KTG

Question

One end of a thermally insulated rod is kept at a temperature ${T_1}$ and the other at ${T_2}$. The rod is composed of two sections of length ${L_1}$ and ${L_2}$ and thermal conductivities ${K_1}$ and ${K_2}$ respectively. The temperature at the interface of the two section is
![](https://imagex.cdn.examgoal.net/y6TIVKiOYjdMNntdZ/Cycn7m9Q4DPie1Q2SaU6IqJCvPQqY/Z6MmVRrMqJ3taBPH74eOLM/image.png)

Accepted Answer

${{{K_1}A\left( {{T_1} - T} ight)} \over {{\ell _1}}} = {{{K_2}A\left( {T - {T_2}} ight)} \over {{\ell _2}}}$
$	herefore$ $T = {{{K_1}{T_1}{\ell _2} + {K_2}{T_2}{\ell _1}} \over {{K_2}{\ell _1} + {K_1}{\ell _2}}}$
$ = {{{K_1}{\ell _2}{T_1} + {K_2}{\ell _1}{T_2}} \over {{K_1}{\ell _2} + {K_2}{\ell _1}}}$
![](https://imagex.cdn.examgoal.net/XvX7bIkAwyLVBh5ng/wfroG7CIxzJcXiNzdrBXsySySq4pJ/B2T95LIqr5rzj6WCRHRbmC/image.svg)

Answer

${{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$

Answer

${{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$

Answer

${{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}$

Answer

${{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}$

Thermodynamics & KTG

One end of a thermally insulated rod is kept at a temperature {T_1} and the other at {T_2}. The rod is composed of two sections of length {L_1} and {L_2} and thermal conductivities {K_1} and {K_2} respectively. The temperature at the interface of the two section is

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