Question

A \(0.5-m^{3}\) rigid tank contains refrigerant- 134 a initially at \(160 \mathrm{kPa}\) and 40 percent quality. Heat is now transferred to the refrigerant until the pressure reaches 700 kPa. Determine (a) the mass of the refrigerant in the tank and ( \(b\) ) the amount of heat transferred. Also, show the process on a \(P\) -v diagram with respect to saturation lines.

Short answer

Question: A rigid tank contains refrigerant-134a initially at a pressure of 160 kPa and a quality of 0.4. The tank is heated until the pressure reaches 700 kPa. Calculate (a) the mass of the refrigerant in the tank, and (b) the amount of heat transferred to the refrigerant. Show the process on a P-v diagram with respect to saturation lines.

Step-by-step solution

Determine the initial specific volume

Using the given pressure, \(P_1 = 160 \,\text{kPa}\), and quality, \(x_1 = 0.4\), we can determine the initial specific volume \(v_1\). First, let's find the specific volume of saturated liquid, \(v_f\), and saturated vapor, \(v_g\), at \(P_1\) using refrigerant-134a property tables. Next, we can calculate the initial specific volume using the quality as follows: $$ v_1 = v_f + x_1 (v_g - v_f) $$ Step 2: Determine the final specific volume

Determine the final specific volume

The final pressure is given as \(P_2 = 700 \,\text{kPa}\). Since the tank is rigid and the volume remains constant, the final specific volume \(v_2 = v_1\). Step 3: Calculate the mass of refrigerant in the tank

Calculate the mass of the refrigerant

Using the initial specific volume, we can now calculate the total mass of refrigerant in the tank. The volume of the tank is given as \(V = 0.5 \,\text{m}^3\). The mass of the refrigerant \(m = \frac{V}{v_1}\). Step 4: Determine the initial and final internal energies

Determine the initial and final internal energies

We can determine the initial internal energy, \(u_1\), using the initial pressure and quality by finding the internal energy of saturated liquid, \(u_f\), and saturated vapor, \(u_g\), at \(P_1\), and then calculating \(u_1\) as follows: $$ u_1 = u_f + x_1 (u_g - u_f) $$ Now, the final specific volume \(v_2\) lies in the superheated region at \(P_2\). We can determine the final internal energy, \(u_2\), by interpolating the refrigerant-134a superheated tables using the final specific volume and pressure. Step 5: Calculate the heat transfer

Calculate the heat transfer

Using the initial and final internal energies, we can now determine the amount of heat transferred for the process, \(Q_{in}\), as follows: $$ Q_{in} = m (u_2 - u_1) $$ Step 6: Plot the process on a P-v diagram

Plot the process on a P-v diagram

To plot the process on a P-v diagram, mark the initial point (\(P_1\), \(v_1\)) in the two-phase region and final point (\(P_2\), \(v_1\)) in the superheated region. Draw the saturation lines for refrigerant-134a using property tables. Lastly, connect the initial and final points with a straight line since the specific volume remains constant in a rigid tank.