A small copper sphere of radius and mass is initially at and is suspended in a large…
PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A small copper sphere of radius 2.0cm and mass 0.20kg is initially at 500K and is suspended in a large evacuated enclosure whose walls are maintained at 300K. The emissivity of the sphere is 0.60 and the specific heat capacity of copper is 385J kg−1K−1. Assume that the sphere loses heat only by radiation and its temperature remains uniform throughout.
(i) Set up the differential equation governing the rate of cooling of the sphere.
(ii) Integrate the equation to obtain an expression for the time required for the sphere to cool from an initial temperature T1 to a final temperature T2.
(iii) Using the expression from part (ii), calculate the time required for the sphere to cool from 500K to 350K. Take the Stefan constant σ=5.67×10−8W m−2K−4.