Question

A tank whose volume is unknown is divided into two parts by a partition. One side of the tank contains \(0.03 \mathrm{m}^{3}\) of refrigerant-134a that is a saturated liquid at 0.9 MPa, while the other side is evacuated. The partition is now removed, and the refrigerant fills the entire tank. If the final state of the refrigerant is \(20^{\circ} \mathrm{C}\) and \(280 \mathrm{kPa}\), determine the volume of the tank.

Short answer

Answer: The volume of the tank is approximately 3.386 m³.

Step-by-step solution

Find the initial specific volume of the refrigerant

Given that the refrigerant exists as a saturated liquid at 0.9 MPa, we can consult the saturation property tables for refrigerant-134a to find the specific volume. From the table, the initial specific volume (\(v_1\)) corresponding to a pressure of 0.9 MPa is given as: \(v_1 = 0.000748 \,\mathrm{m^3/kg}\).

Calculate the initial mass of the refrigerant

Given the initial volume (0.03 m^3) and the specific volume found in step 1, we can now compute the initial mass of the refrigerant with the following formula: \(m_1 = \frac{V_1}{v_1}\), where \(V_1=0.03 \,\mathrm{m^3}\). Substituting the values: \(m_1 = \frac{0.03}{0.000748} \approx 40.11 \,\mathrm{kg}\).

Find the final specific volume of the refrigerant

Given that the final state of the refrigerant is \(20^{\circ} \mathrm{C}\) and \(280 \mathrm{kPa}\), we will use the property tables of refrigerant-134a at this state to find the specific volume (\(v_2\)). From the table, the corresponding specific volume at these conditions is given as: \(v_2 = 0.08447 \,\mathrm{m^3/kg}\).

Calculate the final volume of the refrigerant

The mass of the refrigerant remains constant before and after removing the partition. Therefore, we use mass conservation and the final specific volume to calculate the final volume (\(V_2\)) of the refrigerant: \(V_2 = m_1 \cdot v_2\), Substituting the initial mass and final specific volume found in previous steps: \(V_2 = 40.11 \cdot 0.08447 \approx 3.386 \,\mathrm{m^3}\).

Determine the volume of the tank

The final volume of the refrigerant is equal to the volume of the tank when the partition is removed. Thus, the volume of the tank is given by: \(V_\mathrm{tank} = V_2 \approx 3.386 \,\mathrm{m^3}\).