Question 396: Thermodynamics & KTG

Question

The temperature $$	heta$$ at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures $$	heta$$1 and $$	heta$$2 (as shown in figure) is given by :

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 R1 and R2 as well as top and bottom temperatures \theta1 and \theta$2 (as shown in figure) is given by :

Choose the correct answer: