A wall is made of equally thick layers $P$ and $Q$ of different materials. Thermal conductivity of $Q$ is half of that of the $P$. In the steady state, if the temperature difference across the wall is $24^{\circ} \mathrm{C}$, then the temperature difference across the layer ' $P$ ' is ............…

Question

A wall is made of equally thick layers $P$ and $Q$ of different materials. Thermal conductivity of $Q$ is half of that of the $P$. In the steady state, if the temperature difference across the wall is $24^{\circ} \mathrm{C}$, then the temperature difference across the layer ' $P$ ' is ............... .

Aicharya · Accepted Answer

We have, $ \begin{array}{ll} K_Q=\frac{K_P}{2} \Rightarrow K_P=2 K_Q & \frac{2 K_Q a\left(T_1-T_0\right)}{x}=\frac{K_Q a\left(T_0-T_2\right)}{x} \\ \frac{}{x} & {\left[\because\left[\frac{Q}{t}\right]_P=\left[\frac{Q}{t}\right]_Q\right]} \\ 2\left(T_1-T_0\right)=T_0-T_2 & \end{array} $

According to the question,

Now, from Eq. (i), $ \begin{aligned} & 2 T_1-3 T_0+T_1-24=0 \\ & \Rightarrow \quad 3 T_1-3 T_0=24 \Rightarrow T_1-T_0=8^{\circ} \mathrm{C} \end{aligned} $

A wall is made of equally thick layers $P$ and $Q$ of different materials. Thermal conductivity of $Q$ is…

Solution