Question

A \(5-\mathrm{ft}^{3}\) rigid tank initially contains refrigerant- \(134 \mathrm{a}\) at 60 psia and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant- 134 a at 140 psia and \(80^{\circ} \mathrm{F}\). The valve is now opened, allowing the refrigerant to enter the tank, and is closed when it is observed that the \(\operatorname{tank}\) contains only saturated liquid at 100 psia. Determine (a) the mass of the refrigerant that entered the tank, ( \(b\) ) the amount of heat transfer with the surroundings at \(70^{\circ} \mathrm{F}\), and \((c)\) the entropy generated during this process.

Short answer

Question: Determine the mass of refrigerant-134a that entered the tank, the amount of heat transfer with the surroundings, and the entropy generated during the process, given a rigid tank filled with refrigerant-134a, an initial state of 60 psia and 100% quality, a final state of saturated liquid at 100 psia, a supply line state of 140 psia and 80°F, and a tank volume of 8 ft³. Assume the process takes place at 70°F.

Step-by-step solution

Determine the initial state of the refrigerant in the tank

The initial state of the refrigerant is given as 60 psia and 100% quality. Using the refrigerant-134a tables, we can find the specific volume and the specific enthalpy of the refrigerant in this state.

Calculate the initial mass of refrigerant in the tank

Now that we know the specific volume of the refrigerant at the initial state, we can calculate the initial mass of the refrigerant in the tank using the given volume of the tank and the specific volume: Initial mass = (Volume of the tank) / (Initial specific volume)

Determine the final state of the refrigerant in the tank

The final state of the refrigerant is given as saturated liquid at 100 psia. Using the refrigerant-134a tables, we can find the specific volume and the specific enthalpy of the refrigerant in this state.

Calculate the mass of the refrigerant that entered the tank

Using the conservation of mass principle, we can find the mass of the refrigerant that entered the tank: Mass of refrigerant entered = (Final mass of refrigerant in the tank) - (Initial mass of refrigerant in the tank) Remember that the final mass of refrigerant in the tank can be calculated using the final specific volume and the total volume of the tank.

Determine the initial state of the refrigerant in the supply line

The refrigerant in the supply line is at 140 psia and 80°F. Using the refrigerant-134a tables, we can find the specific enthalpy of the refrigerant in the supply line.

Calculate the heat transfer with the surroundings

Using the first law of thermodynamics and knowing the enthalpy of the refrigerant in the initial state, final state, and the supply line, we can calculate the heat transfer with the surroundings: Q = (Mass of refrigerant entered) * (Enthalpy of refrigerant in the supply line - Enthalpy of refrigerant in the final state) + (Initial mass of refrigerant in the tank) * (Final enthalpy - Initial enthalpy)

Find the entropy change of the refrigerant

Using the refrigerant-134a tables, find the specific entropy of the refrigerant in the initial state, final state, and the supply line.

Calculate the total entropy generated during the process

Using the conservation of entropy principle and the specific entropy values we found in the previous step, we can calculate the total entropy generated during the process: Entropy generated = (Mass of refrigerant entered) * (Entropy change of refrigerant in the supply line) + (Initial mass of refrigerant in the tank) * (Final specific entropy - Initial specific entropy) - Q / (70°F + 459.67)