Discussion Forum



1)

Consider a pair of insulating blocks with thermal resistances R1 and R2 as shown in the figure. The temperature θ at the boundary between the two blocks is

632021414_lugyivztrc6x-q.png


A) $\frac{\theta_{1}\theta_{2}\sqrt{R_{1}R_{2}}}{(\theta_{1}+\theta_{2})(R_{1}+R_{2})}$

B) $\frac{\theta_{1}R_{1}+ \theta_{2}R_{2}}{(R_{1}+R_{2})}$

C) $\frac{\left[\left(\theta_{1}+ \theta_{2}\right) R_{1}R_{2}\right]}{\left(R_1^2+ R_2^2\right)}$

D) $\frac{\left(\theta_{1}R_{2}+ \theta_{2}R_{1}\right)}{R_{1}+ R_{2}}$

Answer:

Option D

Explanation:

Rate of transmission of heat

=$\frac{Temperature difference}{Thermal resistance}$

$\frac{dQ}{dt} = \frac{d\theta}{R}$

Here, $\frac{dQ}{dt}$

= $\frac{\theta - \theta_{2}}{R_{2}} = \frac{\theta_{1}-\theta}{R_{1}}$

= $R_{1}\theta - R_{1}\theta_{2}$ = $R_{2}\theta_{1} - R_{2}\theta$

θ = $\frac{\left(R_{2}\theta_{1} + R_{1}\theta_{2}\right)}{R_{1}+R_{2}}$