In a steady state,the temperature at the end | vedclass

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(A) At steady state,the temperature at different parts of the rod remains constant and is independent of time. The temperature gradient,which is the r

Vedclass · Accepted Answer

$55$

Vedclass · Answer

(A) At steady state,the temperature at different parts of the rod remains constant and is independent of time. The temperature gradient,which is the ratio of the temperature difference to the distance between two points,is constant throughout the rod.Let $T_C$ be the temperature at a point $C$ located $9 \ cm$ from end $A$.The temperature gradient is given by:$\frac{T_A - T_C}{x_C - x_A} = \frac{T_A - T_B}{L}$Substituting the given values:$\frac{100 - T_C}{9} = \frac{100 - 0}{20}$$\frac{100 - T_C}{9} = \frac{100}{20}$$100 - T_C = 5 	imes 9$$100 - T_C = 45$$T_C = 100 - 45 = 55^{\circ} C$Therefore,the temperature at the point is $55^{\circ} C$.

In a steady state,the temperature at the end $A$ and end $B$ of a $20 \ cm$ long rod $AB$ are $100^{\circ} C$ and $0^{\circ} C$. The temperature of a point,$9 \ cm$ from $A$ is (in $^{\circ} C$)

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