A rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2K$ at endAto $K$ at the other end $B$. The endsA and $B$ of the rod are maintained at constant temperature $100^o C$ and $0^o C$, respectively. At steady state, the graph of temperature : $T = T(x)$ where $x =$ distance from end $A$ will be

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is

The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40 \,W$ in the arrangement $(a)$. Find the rates of heat flow when the rods are joined as in arrangement $(b)$ is ......... $W$ (Assume $K_al=200 \,W / m ^{\circ} C$ and $\left.K_{c u}=400 \,W / m ^{\circ} C \right)$

Three identical rods $AB$, $CD$ and $PQ$ are joined as shown. $P$ and $Q$ are mid points of $AB$ and $CD$ respectively. Ends $A, B, C$ and $D$ are maintained at $0^o C, 100^o C, 30^o C$ and $60^o C$ respectively. The direction of heat flow in $PQ$ is

The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\  C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$

As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2 K$ are joined together to form a compound plate. The thickness of plates are $4.0 \,cm$ and $2.5 \,cm$ respectively and the area of cross-section is $120 \,cm ^{2}$ for each plate. The equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha}\right) K$, then the value of $\alpha$ will be_______