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
$\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$
$\frac{\theta_{1} R _{2}-\theta_{2} R _{1}}{ R _{2}- R _{1}}$
$\frac{\theta_{1} R _{2}+\theta_{2} R _{1}}{ R _{1}+ R _{2}}$
$\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$
Three rods of the same dimension have thermal conductivities $3K$ , $2K$ and $K$ . They are arranged as shown in fig. Given below, with their ends at $100^oC, 50^oC $and $20^oC$. The temperature of their junction is ......... $^oC$
An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figure
In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.
In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.
In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.
In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.
The quantity of heat which crosses unit area of a metal plate during conduction depends upon
Ice starts forming in lake with water at ${0^o}C$ and when the atmospheric temperature is $ - {10^o}C$. If the time taken for $1 \;cm$ of ice be $7$ hours, then the time taken for the thickness of ice to change from $1\; cm$ to $2\; cm$ is
Five identical rods are joined as shown in figure. Point $A$ and $C$ are maintained at temperature $120^o C$ and $20^o C$ respectively. The temperature of junction $B$ will be....... $^oC$