The temperature θ at the junction of two insulating sheets, having thermal resistances R 1 and R 2 as well as top and bottom temperatures θ1 and θ2 (as shown in figure) is given by:

Question

The temperature θ at the junction of two insulating sheets, having thermal resistances R 1 and R 2 as well as top and bottom temperatures θ1 and θ2 (as shown in figure) is given by: <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/7679747b1ce95f7b111c9c99776e9146-.png" /> (A) (θ2 R 2-θ1 R 1/ R 2- R 1) (B) (θ1 R 2-θ2 R 1/ R 2- R 1) (C) (θ1 R 2+θ2 R 1/ R 1+ R 2) (D) (θ1 R 1+θ2 R 2/ R 1+ R 2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e98383b92fa75587134192f4a28852c4-.png" /> Heat flow rate will be same through bot ∴ (θ1-θ/ R 1)=(θ-θ2/ R 2) R 2 θ1- R 2 θ= R 1 θ- R 1 θ2 θ=( R 2 θ1+ R 1 θ2/ R 1+ R 2)

Q. The temperature $θ$ at the junction of two insulating sheets, having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $θ_{1}$ and $θ_{2}$ (as shown in figure) is given by :

$\frac{θ _{2} R _{2} - θ _{1} R _{1}}{R _{2} - R _{1}}$

$\frac{θ _{1} R _{2} - θ _{2} R _{1}}{R _{2} - R _{1}}$

$\frac{θ _{1} R _{2} + θ _{2} R _{1}}{R _{1} + R _{2}}$

$\frac{θ _{1} R _{1} + θ _{2} R _{2}}{R _{1} + R _{2}}$

Heat flow rate will be same through bot
$∴ \frac{θ _{1} - θ}{R _{1}} = \frac{θ - θ _{2}}{R _{2}}$
$R_{2} θ_{1} - R_{2} θ = R_{1} θ - R_{1} θ_{2}$
$θ = \frac{R _{2} θ _{1} + R _{1} θ _{2}}{R _{1} + R _{2}}$

Q. The temperature θ at the junction of two insulating sheets, having thermal resistances R1​ and R2​ as well as top and bottom temperatures θ1​ and θ2​ (as shown in figure) is given by :

R2​−R1​θ2​R2​−θ1​R1​​

R2​−R1​θ1​R2​−θ2​R1​​

R1​+R2​θ1​R2​+θ2​R1​​

R1​+R2​θ1​R1​+θ2​R2​​