As the temperature increases, the thermal conductivity of a gas

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by $$k = {k_0} + bT;$$ where $${k_0}$$ and $$b$$ are positive constants, and $$T$$ is temperature.

As $$x$$ increases, the state temperature gradient $$(dT/dx)$$ will

Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \le x \le L} \right),$$ through a planewall with the boundary surfaces $$(x=0$$ and $$x=L)$$ maintained at temperatures of $${0^ \circ }C$$ and $${100^ \circ }C$$. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.

A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding is $$5$$ $$W/{m^2}K.$$ It is propsed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of $$0.05$$ $$W/mK$$. Which one of the following statements is TRUE?