Three rods made of the same material and havi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the temperature of the junction be $	heta$. Since rods $B$ and $C$ are connected in parallel to rod $A$,we can calculate the equivalent therm

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) Let the temperature of the junction be $	heta$. Since rods $B$ and $C$ are connected in parallel to rod $A$,we can calculate the equivalent thermal resistance of the parallel combination of $B$ and $C$. Let the thermal resistance of each rod be $R$. Since rods $B$ and $C$ are in parallel,their equivalent resistance $R_p$ is given by $\frac{1}{R_p} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$,which implies $R_p = \frac{R}{2}$. Now,the system acts as two resistances $R$ and $\frac{R}{2}$ in series. The rate of heat flow $\frac{dQ}{dt}$ through the junction must be conserved. Thus,the heat flowing from the $90^{\circ}C$ ends through the parallel combination must equal the heat flowing through rod $A$ to the $0^{\circ}C$ end. Using the formula $\frac{dQ}{dt} = \frac{\Delta T}{R_{eq}}$: $\frac{90 - 	heta}{R/2} = \frac{	heta - 0}{R}$ $2(90 - 	heta) = 	heta$ $180 - 2	heta = 	heta$ $3	heta = 180$ $	heta = 60^{\circ}C$.

Similar Questions

Two rods having the same cross-sectional area are used to connect two reservoirs at temperatures $100\,^{\circ}C$ and $0\,^{\circ}C$ as shown. The temperature of the junction is $70\,^{\circ}C$. If the rods are now interchanged,the temperature of the junction will be ......... $^{\circ}C$.

Consider the situation as shown in the figure. Find the amount of heat flowing per second through a cross-section of the bent part,if the total heat taken out per second from the end at $200^{\circ} C$ is $150 \ J/s$.

Two identical square metal rods are welded end-to-end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If they are joined as shown in figure $(b)$,the same amount of heat will flow in ...... minutes.

Find the temperature difference between $B$ and $C$. (All rods are identical)

Three rods of identical dimensions are connected as shown in the figure. Points $P$ and $Q$ are maintained at different temperatures. If the rate of heat flow through $PRQ$ and $PQ$ is the same,then...

Vedclass Test Series

Exam Paper Generator

Online Exam Module