   Chapter 10, Problem 17P

Chapter
Section
Textbook Problem

The density of lead is 1.13 × 104 kg/m3 at 20.0°C. Find its density at 105°C.

To determine
The density ( ρ ) at temperature T=105οC .

Explanation

Given Info: Density of lead ( ρ0 ) is 1.13×104kgm3 at T0=20.0οC . The co-efficient of linear expansion of lead ( α ) is 2.9×105/οC

Formula to calculate the density is,

ρ=MV      (I)

• M is the mass.
• V is the volume.

The formula for volume is,

V=V0[1+β(TT0)]       (II)

• β is the co-efficient of volume expansion.

The relation between α and β is,

β=3α

Substitute 3α for β in Equation (II),

V=V0[1+3α(TT0)]       (III)

Substitute Equation (III) in (I),

ρ=MV0[1+3α(TT0)]       (IV)

At temperature T0 ,

ρ0=MV0       (V)

From Equations (IV) and (V),

ρ=ρ0[1+3α(TT0)]

Substitute 2

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