Question

Refrigerant-134a enters the expansion valve of a refrigeration system at 120 psia as a saturated liquid and leaves at 20 psia. Determine the temperature and internal energy changes across the valve.

Short answer

Answer: To determine the temperature and internal energy changes of Refrigerant-134a across the expansion valve, you need to follow these steps: 1. Find the initial properties (T1 and u1) of the refrigerant as a saturated liquid at 120 psia. 2. Assuming an isenthalpic expansion, find the final properties (T2 and u2) of the refrigerant at 20 psia with the same enthalpy. 3. Calculate the change in temperature (ΔT = T2 - T1) and internal energy (Δu = u2 - u1). Please note that you will need a refrigerant property table or thermodynamics software to find the specific properties at the given pressures.

Step-by-step solution

Determine initial properties of the refrigerant as a saturated liquid at 120 psia

Using a refrigerant property table or a thermodynamics software, look up the properties of Refrigerant-134a at 120 psia and as a saturated liquid. Find the corresponding temperature and internal energy (usually denoted as u) at this condition. Let's call these values T1 and u1.

Determine final properties of the refrigerant after expansion at 20 psia

The refrigerant exits the expansion valve at 20 psia, but we are not told the state (saturated liquid, saturated vapor or somewhere between). However, it is reasonable to assume that the refrigerant undergoes an isenthalpic expansion across the valve, since the expansion valve is a throttling device with negligible heat transfer and no work done. Therefore, we will assume that the enthalpy (usually denoted as h) remains constant, i.e., h2 = h1. Now, using a refrigerant property table or thermodynamics software, look up the properties of Refrigerant-134a at 20 psia and the given enthalpy h2 = h1. Find the corresponding temperature and internal energy (u) at this condition. Let's call these values T2 and u2.

Calculate the change in temperature and internal energy

Now that we have the initial and final properties, we can calculate the temperature and internal energy changes across the valve by finding the difference between the initial and final values. Calculate the change in temperature as ΔT = T2 - T1, and the change in internal energy as Δu = u2 - u1. Once you've calculated these values, you'll have the temperature and internal energy changes across the expansion valve for Refrigerant-134a.

Key concepts

Isenthalpic Process

In thermodynamics, when we discuss processes that occur in a fluid, such as a refrigerant, it's important to understand how energy variations take place. An isenthalpic process is key to this understanding, especially in refrigeration systems. This term stems from 'iso-', meaning 'equal,' and 'enthalpy,' which in thermodynamics is a measure of the total heat content of a system.
During an isenthalpic process, the enthalpy of the refrigerant remains constant. This is typical for changes that occur across an expansion valve in a refrigeration cycle. This valve allows the refrigerant to pass from a high-pressure zone to a low-pressure one without exchanging heat with its surroundings or doing external work.
Understanding this concept is crucial because the properties of the refrigerant, such as temperature and internal energy, will change during the expansion, yet the enthalpy does not. This is because the energy due to pressure and volume (common parts of enthalpy calculations) does not externally change, so the internal measurements of the substance transition in a way that keeps the enthalpy stable.
For students tackling problems involving expansion valves, assuming that the process is isenthalpic simplifies calculations. It allows one to use initial enthalpy values to find other properties after expansion by referring to standard refrigerant property tables. Moreover, recognizing this process helps in predicting the behavior of refrigerants and the performance of refrigeration systems.

Refrigerant Properties

Refrigerants are fluids with properties that make them suitable for use in refrigeration and air conditioning systems. The performance of these systems is critically dependent on the thermodynamic properties of the refrigerant involved.
Refrigerant-134a is a commonly used refrigerant and its properties include temperature, pressure, enthalpy, entropy, and internal energy, which can all vary significantly with the physical state (e.g., liquid, vapor) and the conditions of pressure and temperature it's subjected to.
In our specific exercise, Refrigerant-134a enters an expansion valve as a saturated liquid, meaning it is on the verge of vaporization at its current temperature and pressure. It exits the valve at a lower pressure and potentially changes phase. By knowing the pressure and state (such as 'saturated liquid'), you can look up these properties in refrigerant tables or by using software. This data is critical for designing and analyzing refrigeration systems, as it allows for calculations of energy transfer, efficiency, and other important aspects of system performance. Understanding the relationship between pressure, temperature, and other properties of refrigerants is also important for the safe handling and environmental considerations of these substances.

Internal Energy Change

Internal energy is a concept that lies at the heart of understanding thermodynamics and energy exchanges in physical processes. It represents the total energy contained within a substance, comprising both the kinetic energy of particles (atoms, molecules, etc.) and potential energy due to particle interactions.
Change in internal energy can occur during various processes, including the expansion in an expansion valve. In the context of our textbook exercise, understanding the internal energy change across the valve is crucial for analyzing the refrigeration system's performance.
When Refrigerant-134a expands through an expansion valve, there's an alteration of its internal energy, noted as Δu. This is not due to heat addition or work done on the system (since the process is isenthalpic and adiabatic), but primarily due to a change in potential energy as the molecules spread out and move into a larger volume. While the temperature of the refrigerant may drop (as commonly experienced in throttling processes), the internal energy does not necessarily decrease—instead, it can increase, decrease, or remain the same depending on the specific properties of the refrigerant.
For students analyzing this process, it is important to understand that the internal energy change in an isenthalpic process reflects the physical changes the refrigerant undergoes, without energy transfer to or from the surroundings. By applying the principles of conservation of energy within this framework, one can calculate this change (Δu) and predict how the refrigerant will behave downstream of the valve, impacting the remainder of the refrigeration cycle.