A hot body placed in a surrounding of temperature `theta_(0)` obeys Newton's law of cooling `(d theta)/(dt)=-k(theta-theta_(0))` . Its temperature at `t=0` is `theta_(1)` the specific heat capacity of the body is s and its mass is m. Find (a) the maximum heat that the body can lose and (b) the time starting from `t=0` in which it will lose 90% of this maximum heat.

Answer

A, B

Explanation

Given :
Heat capacity `= m xx s = 8-J/^@C`
`((dtheta)/(dt))_(increases) = 2^@C/s`
`((dtheta)/(dt))_(decreases) = 0.2^@C/s`
(a) `Power of heater = mS ((dtheta)/(dt))_(increases)`
`= 80 xx 2 = 160 W`
(b) Power of radiated
`= mS ((dtheta)/(dt))+(decreases)`
`= 80 xx 0.2 = 16 W`.
(c) Now, `m ((dtheta)/(dt)_(decreases) = K (T-T_(0)`
`implies 16 = K(30 - 20)`
`implies K + 16/10 = 1.6`
Now `((dtheta)/(dt)) = K (T-T_0) = 1.6 xx (30 - 25)`
`= 1.6 xx 5 = 8 W`.