A cylindrical block of length and cross-sectional area is placed coaxially on a thin…

PHYSICS · Numerical · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

A cylindrical block of length

0.4\text{ m}

and cross-sectional area

0.04\text{ m}^2

is placed coaxially on a thin metal disc of mass

0.4\text{ kg}

and the same cross-sectional area. The upper face of the cylinder is maintained at a constant temperature of

400\text{ K}

and the initial temperature of the disc is

300\text{ K}

. If the thermal conductivity of the cylinder is

10\text{ W m}^{-1}\text{K}^{-1}

and the specific heat capacity of the disc is

600\text{ J kg}^{-1}\text{K}^{-1}

, how long will the disc take to reach

350\text{ K}

? Assume that the disc has very high thermal conductivity and the system is thermally insulated except for the upper face of the cylinder.