A 0.1-m^3 rigid tank initially contains refrigerant- 134 a at 1.2 MPa and 100 percent quality. T

step 1 Hi everyone, mass of liquid entering into the tank. It is M2 minus M1, that is B upon alpha 2 mi

A 0.1-m^3 rigid tank initially contains refrigerant- 134 a...

A $0.1-m^{3}$ rigid tank initially contains refrigerant- $134 a$ at $1.2 \mathrm{MPa}$ and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant- $134 \mathrm{a}$ at $1.6 \mathrm{MPa}$ and $30^{\circ} \mathrm{C}$. The valve is now opened, allowing the refrigerant to enter the tank, and it is closed when the tank contains only saturated vapor at 1.4 MPa. The refrigerant exchanges heat with a source at $200^{\circ} \mathrm{C}$ during this process. The surroundings are at $15^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. Determine $(a)$ the mass of the refrigerant that entered the tank and $(b)$ the exergy destroyed during this process.

Key Concepts

Irreversibility

Irreversibility in thermodynamic processes refers to the inherent losses that occur due to factors such as friction, turbulence, unrestrained expansion, and finite temperature differences during heat transfer. This concept underpins the calculation of exergy destruction, which quantifies the degradation of energy quality. Recognizing irreversibility is key in both designing more efficient systems and in performing energy and exergy balances accurately.

Exergy Analysis

Exergy analysis is a method used to quantify the maximum useful work that can be obtained from a system, indicating how far a process is from ideal reversible operation. The exergy destruction, which represents the lost work potential due to irreversibilities such as friction, heat transfer across finite temperature differences, and other non-ideal effects, is a central concept in this type of analysis. This concept is vital for understanding the efficiency of energy conversion processes and for identifying areas for improvement.

Phase Change and Quality

Phase change refers to the process of a substance transitioning between liquid and vapor phases. The concept of quality (or vapor fraction) is critical when analyzing mixtures of liquid and vapor, as it quantifies the proportion of the mass in the vapor phase. In problems where the system transitions to a state of pure saturated vapor, understanding quality helps determine the final mass and energy state of the refrigerant.

Mass Balance

Mass balance is a fundamental principle used to determine the amount of substance that enters or leaves a control volume. In a closed system with a changing mass, such as a tank receiving additional refrigerant, the mass balance allows one to equate the initial mass plus the mass added to the final mass determined by properties under equilibrium conditions. This concept is essential for determining how much refrigerant must be added to achieve a desired state.

Rigid Tank Process

A rigid tank process is one in which the volume of the system remains constant throughout the process. This concept is crucial because it implies that any processes occurring inside the tank occur at constant volume, which affects how pressure and temperature change as mass is added or removed. It also means that no work is done by volume change, focusing the analysis on mass and energy balances without expansion work.

Thermodynamic State Properties

Understanding thermodynamic state properties involves knowing the variables that define the state of a substance, such as pressure, temperature, and quality (vapor fraction). These properties are necessary to use property tables and relations, especially when a substance undergoes phase change or when precise conditions like 'saturated vapor at a given pressure' need to be identified. It forms the basis for all calculations in thermodynamic processes.

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