At 0^ C , the density of water is 0.998 g cm ⁻³ , while at 4^ C it is 1.000 g cm ⁻³ . Determine the average coefficient of volume expansion of water over the temperature range of 0 to 4^ C .

Step-by-step solution

The relation between volume and temperature is given by: V₂ = V₁(1 + T) Since mass m remains constant, volume is inversely proportional to density ( V = m ). Substituting this into the equation, we get: m ₂ = m ₁ (1 + T) ₁ ₂ = 1 + T Substituting the given values ₁ = 0.998 g cm ⁻³ at 0^ C , ₂ = 1.000 g cm ⁻³ at 4^ C , and T = 4^ C : 0.998 1.000 = 1 + (4) 0.998 = 1 + 4 4 = 0.998 - 1 4 = -0.002 = -0.0005 ^ C ⁻¹ = -5 10⁻⁴ ^ C ⁻¹