question_answer

Heat is flowing steadily from A to B temperature T at P, at distance x from A is such that                

A) T Decreases linearly with x

B) T Increases linearly with x

C) T Decreases exponentially with x

D) T increases with \[x\]as \[T\propto {{x}^{2}}\]

Correct Answer: B

Solution :

[b]

\[{{\operatorname{T}}_{h}}\]= Higher temperature

\[{{\operatorname{T}}_{1}}\]= Lower temperature

Heart current \[\operatorname{H}=\frac{\Delta Q}{\Delta t}=\frac{KA({{T}_{h}}-{{T}_{l}})}{l}=\frac{KA({{T}_{h}}-T)}{x}\]

\[\Rightarrow \]\[\frac{x}{l}({{T}_{h}}-{{T}_{l}})={{\operatorname{T}}_{h}}-T\]

\[\Rightarrow \]\[T={{T}_{h}}-\left( \frac{{{T}_{h}}-{{T}_{l}}}{l} \right)x\]

\[\Rightarrow \]T Decreases linearly with x from \[{{T}_{h}}\] to \[{{T}_{l}}\]