In steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are 100° C and 0° C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod?

Question

In steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are 100° C and 0° C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod? (A)  5° C  (B)  70° C  (C)  - 30° C  (D)  -50° C

Tardigrade Admin · Accepted Answer

The given condition can be shown as In steady state, the temperature gradient is constant ∴ ((θ A-θ C)/6)=((θ A-θ B)/20) ⇒ (100-θ C)=(6/20)(100-0) ⇒ (100-θ C)=30 or θ C=100-30=70° C

Q. In steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are $100^{\circ} C$ and $0^{\circ} C$ respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod?

$5^{\circ} C$

$70^{\circ} C$

$- 30^{\circ} C$

$- 50^{\circ} C$

The given condition can be shown as
In steady state, the temperature gradient is constant $∴$ $\frac{( θ _{A} - θ _{C} )}{6} = \frac{( θ _{A} - θ _{B} )}{20}$ $\Rightarrow$ $(100 - θ_{C}) = \frac{6}{20} (100 - 0)$ $\Rightarrow$ $(100 - θ_{C}) = 30$ or $θ_{C} = 100 - 30 = 70^{\circ} C$

Q. In steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are 100∘C and 0∘C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod?

5∘C

70∘C

−30∘C

−50∘C