1. Tardigrade
  2. Question
  3. Physics
  4. A slab X of thickness 't', thermal conductivity 'K' and area of cross-section 'A' is placed in thermal contact with another slab Y which is 2n2 times thicker, 4n times conductive and having n times larger cross section area. If the outside face of X is maintained at 100° C, the outside face of Y at 0° C, then the temperature (.t.) of the junction is represented by the graph (.n>0.) :

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Q. A slab $X$ of thickness $'t',$ thermal conductivity $'K'$ and area of cross-section $'A'$ is placed in thermal contact with another slab $Y$ which is $2n^{2}$ times thicker, $4n$ times conductive and having n times larger cross section area. If the outside face of $X$ is maintained at $100^\circ C,$ the outside face of $Y$ at $0^\circ C,$ then the temperature $\left(\right.t\left.\right)$ of the junction is represented by the graph $\left(\right.n>0\left.\right)$ :

NTA AbhyasNTA Abhyas 2022

Solution:

At equilibrium: $\overset{\cdot }{Q}_{1}=\overset{\cdot }{Q}_{2}$
$\Rightarrow \frac{K A \left(\right. t - 0 \left.\right)}{\ell }=\frac{4 n k A n \left(\right. 100 - t \left.\right)}{2 n^{2} \ell }$
$\Rightarrow t=\frac{200}{3}^\circ C$