The ends of copper rod of length `1m` and area of cross section `1cm^(2)` are maintained at `0^(@)C` and `100^(@)C`. At the centre of rod, there is a source of heat of `32W`. The thermal conductivity of copper is `400W//mK`

Options

A. The temperature of rod at centre is `250^(@)C`
B. The temperature of rod at centre is `50^(@)C`
C. The temperature gradient in right half is `500^(@)C//m`
D. The temperature gradient in left half is `300^(@)C//m`

Answer

A, C, D

Explanation

Since there is no accumulation of energy
`(400xx10^(-4)(100-theta))/(1//2)+32=(400xx10^(-4)theta)/(1//2)`
`theta=250^(@)C`
temperature gradient in right half
`=250/(1//2)=300^(@)C//m`
similarly in left half
`=(250-100)/(1//2)=300^(@)C//m`