Question

The coefficient of thermal expansion of water at 25°C is 2.572 × 10⁻⁴ K⁻¹, and its isothermal compressibility is 4.525 x 10⁻⁵ bar⁻¹. Calculate the value of Cₚ-Cᵥ for one mole of water at 25°C. The density of water at 25°C is 0.99705 g.mL⁻¹.

Answer 1

To calculate Cₚ-Cᵥ for one mole of water at 25°C, use the formula Cₚ-Cᵥ = αV₀β. Substitute the given values and calculate the result.

Step-by-step explanation:

To calculate the value of Cₚ-Cᵥ for one mole of water at 25°C, we need to use the formula:

Cₚ-Cᵥ = αV₀β

Where:

• Cₚ is the heat capacity of water at constant pressure
• Cᵥ is the heat capacity of water at constant volume
• α is the coefficient of thermal expansion of water
• V₀ is the volume of one mole of water
• β is the isothermal compressibility of water

First, we need to find the volume of one mole of water at 25°C:

V₀ = 1/density = 1/0.99705 g.mL⁻¹ = 1.003 g.mL⁻¹ = 1.003 x 10⁻³ L

Next, we substitute the values into the formula:

Cₚ-Cᵥ = (2.572 x 10⁻⁴ K⁻¹) x (1.003 x 10⁻³ L) x (4.525 x 10⁻⁵ bar⁻¹)

Cₚ-Cᵥ = 1.167 x 10⁻⁹ K⁻¹.bar⁻¹