# Final Volume of R-134a in a Piston-Cylinder Device ## Given Data - **Mass of R-134a,** \( m = 1.02\, \text{kg} \) - **Initial volume,** \( V_1 = .14\, \text{m}^3 \) - **Initial temperature,** \( T_1 = -26.4^\circ\text{C} \) - **Final temperature,** \( T_2 = 100.^\circ\text{C} \) - **Device:** Weighted piston-cylinder (constant pressure) ## Step 1: Find Initial State ### 1. Calculate Initial Specific Volume \[ v_1 = \frac{V_1}{m} = \frac{.14}{1.02} = .1373\, \text{m}^3/\text{kg} \] ### 2. Use R-134a Property Tables At \( T_1 = -26.4^\circ\text{C} \): - From R-134a tables, the saturation pressure \( P_{\text{sat}} \approx 100\, \text{kPa} \). - Saturated liquid specific volume \( v_f \approx .000757\, \text{m}^3/\text{kg} \). - Saturated vapor specific volume \( v_g \approx .3666\, \text{m}^3/\text{kg} \). Since \( v_1 \) is much greater than \( v_f \) and less than \( v_g \), the refrigerant is a **mixture** at -26.4°C. ### 3. Find Initial Pressure Since the volume is fixed with a weighted piston, the pressure is constant. At \( T_1 \), the pressure is the saturation pressure at \( -26.4^\circ\text{C} \): \[ P_1 = P_{\text{sat, at } -26.4^\circ\text{C}} = 100\, \text{kPa} \] ## Step 2: Final State (After Heating to 100°C, at Constant Pressure) - **Final temperature:** \( T_2 = 100.^\circ\text{C} \) - **Pressure:** \( P_2 = P_1 = 100\, \text{kPa} \) Check the phase at final state: From R-134a tables, at \( P = 100\, \text{kPa} \): - \( T_{\text{sat}} = -26.4^\circ\text{C} \) - At \( T_2 = 100^\circ\text{C} \), the refrigerant is **superheated** at 100 kPa. ## Step 3: Find Final Specific Volume From R-134a superheated tables: - At \( P = 100\, \text{kPa} \), \( T = 100^\circ\text{C} \): - \( v \approx .8845\, \text{m}^3/\text{kg} \) ## Step 4: Calculate Final Volume \[ V_2 = m \cdot v_2 = 1.02 \times .8845 = .902\, \text{m}^3 \] ## **Summary Table** | State | T (\( ^\circ\)C) | P (kPa) | v (\( \text{m}^3/\text{kg} \)) | V (\( \text{m}^3 \)) | Phase | |-------|------------------|---------|-------------------------------|----------------------|-----------| | 1 | -26.4 | 100 | .1373 | .14 | Mixture | | 2 | 100. | 100 | .8845 | .902 | Superheated | ## **Final Answer** \[ \boxed{V_2 = .90\, \text{m}^3} \] (Rounded to two decimal places) --- **References:** R-134a refrigerant property tables (superheated and saturated). **Note:** Actual values might vary slightly depending on the refrigerant property source used.