A cylindrical block of length 0.4 m and area of cross-section `0.04 m^2` is placed coaxially on a thin metal disc of mass ` 0.4 kg` and of the same cross - section. The upper face of the cylinder is maintained at a constant temperature of `400 K` and the initial temperature of the disc is `300K`. if the thermal conductivity of the material of the cylinder is `10 "watt"// m.K ` and the specific heat of the material of the disc is `600J//kg.K`, how long will it take for the temperature of the disc to increase to `350 K`? Assume for purpose of calculation the thermal conductivity of the disc to be very high and the system to be thermally insulated except for the upper face of the cylinder.

Answer

`166.32S`

Explanation

`theta` = temperature of disc
`theta_(0)` = constant temperature
Heat input to disc = `(KA(theta_(0) -0))/(I)`
Heat utilised by disc = `ms(d theta)/(dt)`
(where s = specific heat of disc)
`implies ms(d theta)/(dt) = (KA(theta_(0)-0))/(L) implies =underset(0)overset(0.1)int(d"theta)/(theta_(0)-0) = (KA)/(msL) underset(0)overset(t)intdt`
`implies t = (msL)/(KA)ln ((theta_(0) - 300)/(theta_(0)-350)) implies t= 166.32"sec"`