Answer: the at which the bar conducts now is 5 Js⁻¹
Explanation:
Given the data in the question;
we know that; Heat transfer by conduction is given by;
Q ∝ [tex]A / l[/tex]
such that,
[tex]Q_{1}/Q_{2}[/tex] = [tex]A_{1}l_{2} / A_{2}l_{1}[/tex]
[tex]Q_{2} = Q_{1} A_{2}l_{1}/A_{1}l_{2}[/tex]
so
[tex]Q_{2} =[/tex] ( 10 Js⁻¹ × π([tex]\frac{r}{2}[/tex])² × [tex]l[/tex] ) / (πr² × [tex]\frac{l}{2}[/tex])
[tex]Q_{2} =[/tex] ( 10 Js⁻¹ × π([tex]\frac{r^{2} }{4}[/tex]) × [tex]l[/tex] ) / (πr² × [tex]\frac{l}{2}[/tex])
[tex]Q_{2} =[/tex] ( 10 Js⁻¹ × πr² × 1/4 × [tex]l[/tex] ) / (πr² × 1/2 × [tex]l[/tex] )
[tex]Q_{2} =[/tex] ( 10 Js⁻¹ × 1/4) / ( 1/2)
[tex]Q_{2} =[/tex] ( 10 Js⁻¹ × 1/4) / ( 1/2)
[tex]Q_{2} =[/tex] 5 Js⁻¹
Therefore, the at which the bar conducts now is 5 Js⁻¹
