Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$
IIT 2001, Medium
Download our app for free and get started
(b) Let the temperature of junction be $\theta$. Since roads $B$ and $C$ are parallel to each other (because both having the same temperature difference).
Hence given figure can be redrawn as follows
( $\frac{Q}{t} = \frac{{({\theta _1} - {\theta _2})}}{R}$ and ${\left( {\frac{Q}{t}} \right)_{AB}} = {\left( {\frac{Q}{t}} \right)_{BC}}$
==> $\frac{{(90 - \theta )}}{{R/2}} = \frac{{(\theta - 0)}}{R}$
==> $180 - 2\theta = \theta $
==>$\theta = 60^\circ C$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12\,minutes$ when they are jointed in series. If now both the rods are joined in parallel, then the same amount of heat $\Delta Q$ will flow in ........ $\min$View Solution
- 2A body cools from $80^{\circ}\,C$ to $60^{\circ}\,C$ in $5$ minutes. The temperature of the surrounding is $20^{\circ} C$. The time it takes to cool from $60^{\circ}\,C$ to $40^{\circ}\,C$ is........... $s$View Solution
- 3A body initially at $80^o C$ cools to $64^o C$ in $5$ minutes and to $52^o C$ in $10 $ minutes. The temperature of the body after $15$ minutes will be ...... $^oC$View Solution
- 4View SolutionFor proper ventilation of building, windows must be open near the bottom and top of the walls so as to let pass
- 5The 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 byView Solution
- 6A partition wall has two layers $A$ and $B$ in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer $A$ is twice that of layer $B$. If the steady state temperature difference across the wall is $60K$, then the corresponding difference across the layer $A$ is ....... $K$View Solution
- 7$Assertion :$ For higher temperature the peak emission wavelength of a blackbody shifts to lower wavelengths.View Solution
$Reason :$ Peak emission wavelengths of a black body is proportional to the fourth-power of temperature.
- 8Two identical objects $A$ and $B$ are at temperatures $T_A$ and $T_B$ respectively. Both objects are placed in a room with perfectly absorbing walls maintained at temperatures T $({T_A} > T > {T_B}).$ The objects A and B attain temperature $T $ eventually which one of the following is correct statementView Solution
- 9View SolutionIce formed over lakes has
- 10An object kept in a large room having air temperature of $25^{\circ} \mathrm{C}$ takes $12$ minutes to cool from $80^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. The time taken to cool for the same object from $70^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ would be nearly.....$min$View Solution