Problems in Applied Physics for students of Civil Engineering

SET 5, PROBLEM 3 SIMPLIFIED

Problem 3. A silver ball with the radius of 5 mm and the initial temperature of T

1

=60°C is placed

in the air at room temperature (T

∞

=300 K). The convection coefficient is h=20 W·m

-2

·K

-1

and you

can assume that the temperature of the ball is uniform in its whole volume. Determine and plot
the dependence of the temperature of the ball versus time. When will the ball temperature reach

T

2

=305 K? The time constant of heat transfer in the studied case is given by

S

p

hA

VC

ρ

=

τ

where V

and A

S

are the volume and the surface area of the ball, respectively, and C

p

is the specific heat

(per unit mass). The molar specific heat of a solid, C

mol

, is about 3·R where R is gas constant

(R=8.31 J mol

-1

K

-1

), the molar mass of silver is m

Ag

=107.9 g/mol and the density is

ρ=10.5×10

3

kg/m

3

.