The temperature theta at the junction of two | vedclass

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(C) Since the two insulating sheets are in series,the rate of heat flow $(H)$ through both sheets must be the same in the steady state.The rate of hea

Vedclass · Accepted Answer

$\frac{	heta_{1} R_{2}+	heta_{2} R_{1}}{R_{1}+R_{2}}$

Vedclass · Answer

(C) Since the two insulating sheets are in series,the rate of heat flow $(H)$ through both sheets must be the same in the steady state.The rate of heat flow is given by $H = \frac{\Delta 	heta}{R}$.For the first sheet (bottom),the heat flow is $H = \frac{	heta - 	heta_{1}}{R_{1}}$.For the second sheet (top),the heat flow is $H = \frac{	heta_{2} - 	heta}{R_{2}}$.Equating the two rates:$\frac{	heta - 	heta_{1}}{R_{1}} = \frac{	heta_{2} - 	heta}{R_{2}}$$R_{2}(	heta - 	heta_{1}) = R_{1}(	heta_{2} - 	heta)$$R_{2}	heta - R_{2}	heta_{1} = R_{1}	heta_{2} - R_{1}	heta$$R_{2}	heta + R_{1}	heta = R_{1}	heta_{2} + R_{2}	heta_{1}$$	heta(R_{1} + R_{2}) = R_{1}	heta_{2} + R_{2}	heta_{1}$$	heta = \frac{R_{1}	heta_{2} + R_{2}	heta_{1}}{R_{1} + R_{2}}$Thus,the correct option is $C$.

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

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