Question

Refrigerant-134a is throttled from the saturated liquid state at \(700 \mathrm{kPa}\) to a pressure of \(160 \mathrm{kPa}\). Determine the temperature drop during this process and the final specific volume of the refrigerant.

Short answer

Question: Determine the temperature drop and final specific volume of Refrigerant-134a when it undergoes a throttling process from a saturated liquid state at 700 kPa to a pressure of 160 kPa. Answer: To find the temperature drop and final specific volume of Refrigerant-134a, first determine the initial state by looking up the saturation temperature and specific enthalpy at 700 kPa. Apply the isenthalpic process condition to find the final specific enthalpy. Determine the final state by looking up the saturation temperatures, pressures, and specific enthalpies in the property table at a pressure of 160 kPa. Calculate the temperature drop by taking the difference between the initial and final temperatures and find the final specific volume by looking up the final state in the property table.

Step-by-step solution

Determine the initial state

The problem states that the initial state of the refrigerant is a saturated liquid at a pressure of 700 kPa. We can look up the saturation temperature and specific enthalpy at this pressure in a Refrigerant-134a property table. Let's denote the initial temperature as \(T_1\) and the initial specific enthalpy as \(h_1\).

Apply the isenthalpic process condition

Since the throttling process is isenthalpic, the specific enthalpy at the final state (\(h_2\)) is equal to the specific enthalpy at the initial state (\(h_1\)). Mathematically, this can be represented as: \(h_2 = h_1\) We already found \(h_1\) in Step 1, so we have the specific enthalpy for the final state directly from the initial state.

Determine the final state

Now that we have the final pressure \(P_2=160 \mathrm{kPa}\) and the final specific enthalpy \(h_2\), we can find the final state by looking up the saturation temperatures, pressures, and specific enthalpies in the Refrigerant-134a property table. We need to find the final temperature \(T_2\) and specific volume \(v_2\).

Calculate the temperature drop

Now that we have the initial temperature \(T_1\) and final temperature \(T_2\), we can calculate the temperature drop during the throttling process by simply taking the difference between the initial and final temperatures: Temperature drop = \(T_1 - T_2\)

Find the final specific volume

We have already found the final specific volume \(v_2\) in Step 3 while determining the final state. The temperature drop and final specific volume are the answers to this problem.

Key concepts

Refrigerant-134a Properties

Refrigerant-134a, also known as R-134a, is a hydrofluorocarbon (HFC) used widely in air conditioning and refrigeration systems. Understanding its properties is crucial for designing and analyzing such systems. R-134a is non-flammable, non-toxic, and has zero ozone depletion potential, making it an environmentally safer alternative to older refrigerants like R-12.

Key thermophysical properties of R-134a include its boiling point, specific heat, thermal conductivity, viscosity, and more importantly for this exercise, its temperature-enthalpy relationship. These properties vary with pressure and temperature, influencing the refrigerant's performance during phase change processes. For instance, knowing the saturation temperature at a given pressure can help determine the refrigerant's state — whether it's in a liquid, vapor, or mixed phase — which is essential in thermodynamic calculations.

Isenthalpic Process

The isenthalpic process is a vital concept in thermodynamics, particularly relevant in the analysis of throttling devices such as expansion valves and capillary tubes. During an isenthalpic process, the specific enthalpy (\(h\)) remains constant even though other properties like temperature and pressure may change. This is because throttling is an adiabatic process with no work done on or by the system and negligible heat transfer.

In the context of the example problem where Refrigerant-134a is throttled, the process does not change the enthalpy. By assuming that we undergo an ideal, isenthalpic process, we can track and predict the state of the refrigerant after throttling using the initial enthalpy as an anchor point. Recognizing that the final enthalpy equals the initial enthalpy (\(h_2 = h_1\) simplifies calculations in the absence of external heat transfer or work.

Specific Volume

Specific volume (\(v\) is a fundamental property in thermodynamics, defined as the volume occupied by a unit mass of a substance. It is the inverse of density and provides engineers with insights into the space requirements for a system's design and operation. For example, the specific volume of a refrigerant like R-134a can dictate the size of the components, such as pipes and compressors, in a refrigeration cycle.

In the context of refrigeration and air-conditioning systems, the specific volume of the refrigerant changes significantly during phase transitions from liquid to vapor and vice versa. When dealing with the throttling process, as shown in the exercise, understanding specific volume before and after the process is crucial to determine the effect on the refrigerant's density and to ensure proper function of the related thermal system components.

Pressure-Enthalpy Diagram

The pressure-enthalpy (\(P-h\) diagram is a valuable tool in visualizing the thermodynamic processes of refrigerants like R-134a. It plots pressure on the vertical axis and enthalpy on the horizontal axis, showing all the possible states the refrigerant can exist in. Key regions in this diagram include the saturated liquid line, the saturated vapor line, and the superheated vapor region. It also includes constant entropy lines, which are useful in analyzing isentropic processes.

For the throttling process, the pressure-enthalpy diagram helps identify states before and after the process. Since throttling is an isenthalpic process, the initial and final points would lie on a vertical line that corresponds to constant enthalpy. This makes it easier to illustrate and understand the changes in the refrigerant's state during a throttling process, aiding in efficient system design and problem-solving.