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

Rate of cooling `(Delta theta)/(t)=(A epsilon sigma (T^(4)-T_(0)^(4)))/(mc)`
`rArr t prop (m)/(A)[Delta theta, t, sigma, (T^(4)-T_(0)^(4))" are constant"]`
`rArr t prop (m)/(A) prop ("Volume")/("Area") prop (a^(3))/(a^(2)) rArr t prop a rArr (t_(1))/(t_(2))=(a_(1))/(a_(2))`
`rArr (100)/(t_(2))=(1)/(2) rArr t_(2)=200 sec`