Question 338: Thermodynamics & KTG

Question

The temperature $	heta$ at the junction of two insulating sheets, having thermal resistances R
1
and R
2
as well as top and bottom temperatures $	heta$
1
and $	heta$
2
(as shown in figure) is given by :
![](https://imagex.cdn.examgoal.net/1kltqnhrj/ad5afed1-a72d-4088-8193-fc9333b07a7a/54cc63f0-7c49-11eb-98b4-b931446ae6e4/file-1kltqnhrk-206w.jpg)

Accepted Answer

Temperature at the junction is $	heta$.
so using the formula
${{{T_2} - T} \over {{R_1}}} = {{T - {T_1}} \over {{R_2}}}$
${{{	heta _2} - 	heta } \over {{R_2}}} = {{	heta  - {	heta _1}} \over {{R_1}}}$${R_1}({	heta _2} - 	heta ) = {R_2}(	heta  - {	heta _1})$
${R_1}{	heta _2} - {R_1}	heta  = {R_2}	heta  - {R_2}{	heta _1}$
${R_1}	heta  + {R_2}	heta  = {R_1}{	heta _2} + {R_2}{	heta _1}$
$	heta  = {{{R_1}{	heta _2} + {R_2}{	heta _1}} \over {{R_1} + {R_2}}}$

Answer

${{{	heta _1}{R_2} + {	heta _2}{R_1}} \over {{R_1} + {R_2}}}$

Answer

${{{	heta _1}{R_1} + {	heta _2}{R_2}} \over {{R_1} + {R_2}}}$

Answer

${{{	heta _1}{R_2} - {	heta _2}{R_1}} \over {{R_2} - {R_1}}}$

Answer

${{{	heta _2}{R_2} - {	heta _1}{R_1}} \over {{R_2} - {R_1}}}$

Thermodynamics & KTG

The temperature \theta at the junction of two insulating sheets, having thermal resistances R 1 and R 2 as well as top and bottom temperatures \theta 1 and \theta 2 (as shown in figure) is given by :

Choose the correct answer: