Answer:
1.35 × 10⁴ kg/m³ at 22 °C; 1.34 × 10⁴ kg/m³ at 100 °C
Explanation:
The cubic expansivity (γ) of a liquid is the fractional change in volume per unit change in temperature.
[tex]\gamma = (\frac{\Delta V }{ V_0} )(\frac{1 }{ \Delta T} )[/tex] Multiply by V₀ΔT and transpose
ΔV = γV₀ΔT
and
V = V₀ + ΔV
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At 0 °C
Assume you have 1 m³ of Hg
ρ = m/V Multiply by V and transpose
m = ρV
ρ = 1.36 × 10⁴ kg/m³
m = 1.36 × 10⁴ × 1 = 1.36 × 10⁴ kg
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At 22 °C
Assume that you have 1 m³ of Hg
γ = 180 × 10⁻⁶ K⁻¹
ΔT = 22 °C – 0 °C = 22 °C
ΔV = 180 × 10⁻⁶ × 22
ΔV = 3.96 × 10⁻³ m³ Calculate volume
V = 1 + 0.00396
V = 1.00396 m³ Calculate density
ρ = 1.36 × 10⁴/1.00396
ρ = 1.35 × 10⁴ kg/m³
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At 100 °C
ΔT = 100 °C – 0 °C = 100 °C
ΔV = 180 × 10⁻⁶ × 100
ΔV = 0.0180 m³ Calculate volume
V = 1 + 0.0180
V = 1.0180 m³ Calculate density
ρ = 1.36 × 10⁴/1.0180
ρ = 1.34 × 10⁴ kg/m³
