Three rods of same dimensions are arranged as | vedclass

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

Question

(C) The rate of heat flow $H$ is given by $H = \frac{\Delta 	heta}{R_{th}}$,where $R_{th} = \frac{l}{KA}$ is the thermal resistance.For the path $PRQ

Vedclass · Accepted Answer

${K_3} = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}$

Vedclass · Answer

(C) The rate of heat flow $H$ is given by $H = \frac{\Delta 	heta}{R_{th}}$,where $R_{th} = \frac{l}{KA}$ is the thermal resistance.For the path $PRQ$,the rods with conductivities ${K_1}$ and ${K_2}$ are in series. Their equivalent thermal resistance is $R_{PRQ} = \frac{l}{{K_1}A} + \frac{l}{{K_2}A} = \frac{l}{A} \left( \frac{1}{{K_1}} + \frac{1}{{K_2}} ight) = \frac{l}{A} \left( \frac{{K_1} + {K_2}}{{K_1}{K_2}} ight)$.For the path $PQ$,the rod with conductivity ${K_3}$ has thermal resistance $R_{PQ} = \frac{l}{{K_3}A}$.Given that the heat flows at the same rate along both paths,the thermal resistances must be equal: $R_{PRQ} = R_{PQ}$.Therefore,$\frac{l}{A} \left( \frac{{K_1} + {K_2}}{{K_1}{K_2}} ight) = \frac{l}{{K_3}A}$.Simplifying this,we get $\frac{1}{{K_3}} = \frac{{K_1} + {K_2}}{{K_1}{K_2}}$,which implies ${K_3} = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}$.

Similar Questions

Four identical rods of the same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is $100^{\circ}C$,then the temperature difference between the ends of the other diagonal 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 metal rods are welded end-to-end as shown in figure $(1)$. It takes $4 \ min$ for $20 \ cal$ of heat to flow through them. If these rods are now welded side-by-side as shown in figure $(2)$,the time taken for the same amount of heat to flow through them is .......... $\min$.

Two rods of the same length and material are joined end-to-end. They transfer a certain amount of heat in $8 \ s$. When they are joined in parallel,they transfer the same amount of heat under the same conditions in a time of: (in $s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module