Question

A cylindrical bar that us well insulated around its sides connects hot and cold reservoirs and conducts heat at a rate of 10.0 J/s under steady state conditions. If all of its linear dimensions (diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reservoirs is closest to

Answer 1

Answer: the at which the bar conducts now is 5 Js⁻¹

Step-by-step explanation:

Given the data in the question;

we know that; Heat transfer by conduction is given by;

Q ∝
`A / l`

such that,

`Q_(1)/Q_(2)` =
`A_(1)l_(2) / A_(2)l_(1)`

`Q_(2) = Q_(1) A_(2)l_(1)/A_(1)l_(2)`

so

`Q_(2) =` ( 10 Js⁻¹ × π(
`(r)/(2)`)² ×
`l` ) / (πr² ×
`(l)/(2)`)

`Q_(2) =` ( 10 Js⁻¹ × π(
`(r^(2) )/(4)`) ×
`l` ) / (πr² ×
`(l)/(2)`)

`Q_(2) =` ( 10 Js⁻¹ × πr² × 1/4 ×
`l` ) / (πr² × 1/2 ×
`l` )

`Q_(2) =` ( 10 Js⁻¹ × 1/4) / ( 1/2)

`Q_(2) =` ( 10 Js⁻¹ × 1/4) / ( 1/2)

`Q_(2) =` 5 Js⁻¹

Therefore, the at which the bar conducts now is 5 Js⁻¹