Aring consisting of two parts $ADB$ and $ACB$ of same conductivity $k$ carries an amount of heat $H$. The $ADB$ part is now replaced with another metal keeping the temperatures $T_1$ and $T_2$ constant. The heat carried increases to $2H$. What $ACB$ should be the conductivity of the new$ADB$ part? Given $\frac{{ACB}}{{ADB}}= 3$

The wall with a cavity consists of two layers of brick separated by a layer of air.All three layers have the same thickness and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer and steady state condition exists. Which of the following graphs predicts correctly the variation of temperature $T$ with distance $d$ inside the cavity?

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ , respectively are $T_2$ and $T_1$ ($T_2$ > $T_1$). The rate of heat transfer through the slab, in a steady state is $\left( {\frac{{A({T_2} – {T_1})K}}{x}} \right)f$, with $f $ which equal to

Which of the following circular rods. (given radius $ r$ and length $l$ ) each made of the same material as whose ends are maintained at the same temperature will conduct most heat

An iron bar $\left(L_{1}=0.1\; m , A_{1}\right.$ $\left.=0.02 \;m ^{2}, K_{1}=79 \;W m ^{-1} K ^{-1}\right)$ and a brass bar $\left(L_{2}=0.1\; m , A_{2}=0.02\; m ^{2}\right.$ $K_{2}=109 \;Wm ^{-1} K ^{-1}$ are soldered end to end as shown in Figure. The free ends of the iron bar and brass bar are maintained at $373 \;K$ and $273\; K$ respectively. Obtain expressions for and hence compute

$(i)$ the temperature of the junction of the two bars,

$(ii)$ the equivalent thermal conductivity of the compound bar, and

$(iii)$ the heat current through the compound bar.