A metal sphere at is allowed to cool in air maintained at

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A metal sphere at

92^{\circ}\text{C}

is allowed to cool in air maintained at

22^{\circ}\text{C}

. Its temperature drops to

58^{\circ}\text{C}

after

8

minutes. (i) Determine the value of the constant

k

(in

\text{min}^{-1}

) that governs the cooling. (ii) Find the additional time required for the sphere to reach

30^{\circ}\text{C}

(answer in minutes, correct to one decimal place).