Question

In the steady state, the two ends of a metel rod are at ${30}^{o}C$ and ${20}^{o}C$. The temperature at the 60th cm is

• A. ${22}^{o}C$
• B. ${23}^{o}C$
• C. ${24}^{o}C$
• D. ${25}^{o}C$

Answer 1

The correct option is C ${24}^{o}C$

Given the rod is in steady state, and of one meter length.
Temperature gradient is a constant.
$\frac{dT}{dx}=c$
$dT=cdx$
$T=cx+a$; Substituting the conditions that T(0) = 30 and T(100) = 20;
$T=-0.1x+30;$
putting T(60) we get $T\left(60\right)=-6+30={24}^{\circ }C$