# Step-by-Step Solution: Saturation Pressure and Specific Volume of Water at 256°C We are tasked to find: 1. The **saturation pressure** of water at 256°C. 2. The **specific volume of saturated steam** at this pressure (i.e., at 256°C). --- ## 1. Finding Saturation Pressure at 256°C The **saturation pressure** for a given temperature is the pressure at which water boils (liquid and vapor are in equilibrium) at that temperature. This value is typically found in **steam tables**. ### Using Steam Tables Look up the row where the saturation temperature is **256°C**. **From typical steam tables:** | Temperature (°C) | Pressure (MPa) | Pressure (bar) | |------------------|---------------|---------------| | 255 | 3.983 | 39.83 | | **256** | **4.056** | **40.56** | | 257 | 4.130 | 41.30 | **Saturation Pressure at 256°C:** - \( P_{\text{sat, 256°C}} = 4.056 \) MPa - Or \( 40.56 \) bar --- ## 2. Finding Specific Volume at Saturation Pressure The **specific volume** at the saturation temperature and pressure can refer to either: - \( v_f \): Specific volume of saturated liquid (water) - \( v_g \): Specific volume of saturated vapor (steam) Usually, for steam, the **specific volume of saturated vapor (\( v_g \))** is desired. ### From Steam Tables (at 256°C): | Temperature (°C) | \( v_f \) (m³/kg) | \( v_g \) (m³/kg) | |------------------|-------------------|-------------------| | 255 | .001240 | .04837 | | **256** | .001243 | .04797 | | 257 | .001246 | .04757 | - **Specific volume of saturated vapor at 256°C:** \( v_g = .04797 \) m³/kg - **Specific volume of saturated liquid at 256°C:** \( v_f = .001243 \) m³/kg --- ## Final Answers ### 1. Saturation Pressure at 256°C - \( P_{\text{sat}} = 4.056 \) MPa (or **40.56 bar**) ### 2. Specific Volume at Saturation Pressure (256°C) - For vapor (steam): \( v_g = .04797 \) m³/kg - For liquid: \( v_f = .001243 \) m³/kg --- ## Summary Table | Value | At 256°C | |----------------------|------------------| | Saturation Pressure | 4.056 MPa (40.56 bar) | | \( v_f \) (liquid) | .001243 m³/kg | | \( v_g \) (vapor) | .04797 m³/kg | --- **References:** - [Steam Tables (IAPWS-IF97)](https://webbook.nist.gov/chemistry/fluid/) - Standard Thermodynamics textbooks --- **Note:** Values may vary slightly depending on the steam table source, but these are typical. Always use the steam table provided for your course or industry for official calculations.