Calculation of density of turpentine at 373 K

Coefficient of real expansion: Coefficient of real expansion is the fractional change in volume per degree change in temperature at constant pressure. It is denoted by β and has units of K⁻¹.

Given, coefficient of real expansion of turpentine = 9.6 x 10⁻⁴ / °C

Density: Density is defined as the mass per unit volume of a substance. It is denoted by ρ and has units of kg/m³ or g/cm³.

Given, density of turpentine at 0°C = 0.867 g/cm³

Conversion of units: The given density is in g/cm³, but we need to convert it to kg/m³ to use it in our calculation. We can use the conversion factor 1 g/cm³ = 1000 kg/m³.

So, density of turpentine at 0°C = 0.867 x 1000 kg/m³ = 867 kg/m³

Temperature: We need to find the density of turpentine at 373 K.

Coefficient of volumetric expansion: We can use the coefficient of real expansion to calculate the coefficient of volumetric expansion, which is denoted by γ and has units of K⁻¹.

γ = 3β

γ = 3 x 9.6 x 10⁻⁴ / °C = 2.88 x 10⁻³ / °C

Density at 373 K: We can use the formula for volumetric expansion to calculate the density of turpentine at 373 K.

Vf = Vi(1 + γΔT)

where Vf is the final volume, Vi is the initial volume, γ is the coefficient of volumetric expansion, and ΔT is the change in temperature.

Since we are dealing with density, we can rewrite this formula as:

ρf = ρi / (1 + γΔT)

where ρf is the final density and ρi is the initial density.

ΔT = (373 - 273) K = 100 K

ρf = 867 / (1 + 2.88 x 10⁻³ x 100) kg/m³

ρf = 840.5 kg/m³

Conclusion: The density of turpentine at 373 K is 840.5 kg/m³.