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Water at 15°C and 1 atm pressure is heated to 100°C at constant pressure. Using coefficient of volume expansion data, determine the change in the density of water.

Answer :

ONYEBUCHINNAJIGO

The change in density of water is -41.82 kg/m³

The given parameters;

  • initial temperature of the water, = 15°C
  • final temperature of the water, = 100 °C
  • density of water at 1 atm, ρ = 999.9 kg/m³

The change in density of water using coefficient of volume expansion is given as;

[tex]\Delta \rho = -\beta \rho \Delta T[/tex]

where;

[tex]\beta[/tex] is the coefficient of volume expansion of water

the average temperature of 15 °C and 100 °C = 57.5

the coefficient of volume expansion of water = 0.492 x 10⁻⁴ K⁻¹

The change in density of water is calculated as;

[tex]\Delta \rho = -\beta \rho \Delta T\\\\\Delta \rho = -(4.92\times 10^{-4} ) (999.9)(100-15)\\\\\Delta \rho = -41.82 \ kg/m^3[/tex]

Thus, the change in density of water is -41.82 kg/m³

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