# Saturation Pressure and Specific Volume of Water at Given Temperatures Let's solve for the **saturation pressure** and **specific volume** of water at **2°C, 5°C, and 6°C**. ## Step 1: Understanding the Problem - **Saturation pressure**: The pressure at which water boils (liquid and vapor coexist) at a given temperature. - **Specific volume at saturation**: The volume occupied by unit mass of water vapor at saturation conditions. We will use standard thermodynamic steam tables for the calculations. --- ## Step 2: Find Saturation Pressure (\(P_{sat}\)) Look up the saturation pressure corresponding to each temperature. ### **a) At 2°C** From steam tables (values may slightly vary by source): - **Saturation pressure (\(P_{sat}\)) at 2°C**: \(P_{sat} \approx .00706\) bar \(= .706\) kPa ### **b) At 5°C** - **Saturation pressure (\(P_{sat}\)) at 5°C**: \(P_{sat} \approx .00872\) bar \(= .872\) kPa ### **c) At 6°C** - **Saturation pressure (\(P_{sat}\)) at 6°C**: \(P_{sat} \approx .00934\) bar \(= .934\) kPa --- ## Step 3: Find Specific Volume of Saturated Vapor (\(v_g\)) at Each Temperature Specific volume (\(v_g\)) is the volume per kg of water vapor at the saturation pressure. ### **a) At 2°C** - **\(v_g\) at 2°C**: \(v_g \approx 107.48\, \text{m}^3/\text{kg}\) ### **b) At 5°C** - **\(v_g\) at 5°C**: \(v_g \approx 98.63\, \text{m}^3/\text{kg}\) ### **c) At 6°C** - **\(v_g\) at 6°C**: \(v_g \approx 96.16\, \text{m}^3/\text{kg}\) --- ## Step 4: Summary Table | Temperature (°C) | \(P_{sat}\) (bar) | \(P_{sat}\) (kPa) | \(v_g\) (\(\text{m}^3/\text{kg}\)) | |------------------|-------------------|-------------------|----------------------| | 2 | .00706 | .706 | 107.48 | | 5 | .00872 | .872 | 98.63 | | 6 | .00934 | .934 | 96.16 | --- ## Step 5: Final Answers **At 2°C:** - Saturation pressure: \(.00706\, \text{bar}\) (\(.706\, \text{kPa}\)) - Specific volume: \(107.48\, \text{m}^3/\text{kg}\) **At 5°C:** - Saturation pressure: \(.00872\, \text{bar}\) (\(.872\, \text{kPa}\)) - Specific volume: \(98.63\, \text{m}^3/\text{kg}\) **At 6°C:** - Saturation pressure: \(.00934\, \text{bar}\) (\(.934\, \text{kPa}\)) - Specific volume: \(96.16\, \text{m}^3/\text{kg}\) --- ## Step 6: Explanation - **Steam tables** are used to determine the saturation pressure and specific volume at a given temperature. - The specific volume of vapor decreases as temperature increases, because the density of vapor increases with temperature. - The saturation pressure increases rapidly with temperature. --- ## References - Thermodynamic Steam Tables (IAPWS, ASME) - Yunus Çengel & Michael Boles, *Thermodynamics: An Engineering Approach*