Question

A \(0.1-m^{3}\) rigid tank contains saturated refrigerant\(134 \mathrm{a}\) at \(800 \mathrm{kPa}\). Initially, 30 percent of the volume is occupied by liquid and the rest by vapor. A valve at the bottom of the tank is opened, and liquid is withdrawn from the tank. Heat is transferred to the refrigerant from a source at \(60^{\circ} \mathrm{C}\) so that the pressure inside the tank remains constant. The valve is closed when no liquid is left in the tank and vapor starts to come out. Assuming the surroundings to be at \(25^{\circ} \mathrm{C}\) determine \((a)\) the final mass in the tank and \((b)\) the reversible work associated with this process.

Short answer

Question: Determine the final mass of refrigerant in the tank and the reversible work associated with the process. Answer: The final mass of refrigerant in the tank is equal to the initial mass of vapor, \(m_f = m_{vapor}\). The reversible work associated with the process can be calculated using the formula: \(W_{rev} = Q_{in} - (m_i - m_f)h_f\).

Step-by-step solution

Determine the initial mass of refrigerant in the tank

To first find the initial mass of the refrigerant in the tank, we need to find the mass of the liquid and vapor using their respective saturation properties from the refrigerant 134a tables for the given pressure of 800 kPa. As per the problem, the liquid occupies 30 percent of the total volume, while the vapor occupies 70 percent. From the refrigerant 134a saturation table at 800 kPa, we get the specific volume for the saturated liquid (\(v_f\)) and the saturated vapor (\(v_g\)) as: \(v_f = 0.000745\:m^3/kg\) \(v_g = 0.023313\:m^3/kg\) Now we can find the mass of liquid and vapor in the tank: \(V_{liquid} = 0.1\times0.3\:m^3\) \(m_{liquid} = \frac{V_{liquid}}{v_f}\) \(V_{vapor} = 0.1\times0.7\:m^3\) \(m_{vapor} = \frac{V_{vapor}}{v_g}\) Now, add up the masses to get the initial mass (\(m_i\)): \(m_i = m_{liquid} + m_{vapor}\)

Find the final mass in the tank

When the valve is closed, no liquid is left in the tank, which means the final mass must be equal to the initial mass of vapor. The final mass in the tank, \(m_f = m_{vapor}\)

Calculate the enthalpy values

We need to find the enthalpy for saturated liquid (\(h_f\)) and saturated vapor (\(h_g\)) from the refrigerant 134a saturation table at 800 kPa. \(h_f = 212.28\:kJ/kg\) \(h_g = 395.04\:kJ/kg\)

Determine the heat transferred to the refrigerant

We will use the enthalpy values to find the heat transferred to the refrigerant, which can be calculated using the following formula: \(Q_{in} = m_f (h_g - h_f)\)

Calculate the reversible work associated with the process

Since the pressure inside the tank remains constant, the reversible work can be calculated using the following formula: \(W_{rev} = Q_{in} - (m_i - m_f)h_f\) Now substitute the values calculated in the previous steps to get the final mass in the tank and the reversible work associated with the process.