A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from `100^@C` to `99^@C` in 100 s. Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from `100^@C` to `99^@C` will be approximately

Options

A. 25 s
B. 50 s
C. 200 s
D. 400 s

Answer

C

Explanation

`(dT)/(dt)=(eAsigma)/(mc)(T^4-T_0^4)=(e(6a^2)sigma)/((a^3xxrho)c)(T^4-t_0^4)`
`implies` for the same fall in temperature time `dtpropa`
`(dt_2)/(dt_1)=(a_2)/(a_1)=(2cm)/(1cm)impliesdt_2=2xxdt_1=2xx100s=200s`
(As `A=6a^2` and `m=Vxxrho=a_3xxrho`)