Question

Refrigerant-134a at \(800 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\) is throttled to a temperature of \(-20^{\circ} \mathrm{C}\). Determine the pressure and the internal energy of the refrigerant at the final state.

Short answer

Question: A throttling process of refrigerant-134a starts from an initial pressure of 800 kPa and an initial temperature of 25°C and ends at a final temperature of -20°C. Determine the final pressure and internal energy of the refrigerant at the final state. Answer: Using the R134a Tables and the isenthalpic process, the final pressure and internal energy of the refrigerant-134a at -20°C are __(P_2)__ and __(u_2)__, respectively.

Step-by-step solution

Find Initial Properties

Using the R134a Tables, look for the properties of the refrigerant at the given initial conditions: \(800\,\text{kPa}\) and \(25^{\circ}\text{C}\). Note down the specific enthalpy (\(h_1\)) and specific internal energy (\(u_1\)) at this initial state.

Throttling Process

A throttling process is an isenthalpic process, which means the specific enthalpy remains constant. Thus, the specific enthalpy at the final state is the same as the initial state: \(h_2=h_1\).

Find Final Properties

Using the R134a Tables, find the properties of the refrigerant at the final temperature, \(-20^{\circ}\text{C}\), and with the specific enthalpy found in Step 2 (\(h_2=h_1\)). This will give the final pressure (\(P_2\)) and specific internal energy (\(u_2\)).

Determine the Final Pressure and Internal Energy

Using the information obtained in Step 3, state the final pressure (\(P_2\)) and internal energy (\(u_2\)) of the refrigerant at the final state.

Key concepts

Refrigerant-134a Properties

Refrigerant-134a, also known as R-134a, is a hydrofluorocarbon (HFC) commonly used in air conditioning and refrigeration systems. It has gained popularity as a replacement for CFCs and HCFCs which are known to deplete the ozone layer.

Understanding its properties is essential for engineers and technicians working with refrigeration systems. R-134a operates efficiently over a broad range of temperatures and pressures, making it versatile in different climates and applications. Its key thermodynamic properties include specific enthalpy and specific internal energy, which determine the energy content at various states. By utilizing pressure-enthalpy charts or thermodynamic tables for R-134a, professionals can predict how it will behave under changing conditions in a system.

Isenthalpic Process

An isenthalpic process is a thermodynamic process during which the enthalpy of the fluid remains constant. This is a typical characteristic of a throttling process, not common in everyday life, but crucial in the design of refrigeration and air conditioning systems, as well as in other engineering applications.

In the context of the exercise, when Refrigerant-134a is throttled, its enthalpy before and after the process remains the same (\(h_1 = h_2\)). Despite a change in pressure and possibly other properties like temperature, no heat is transferred to or from the refrigerant, and no work is done by or on the refrigerant during throttling.

Internal Energy

The concept of internal energy in thermodynamics refers to the total energy contained within a system, accounting for both the kinetic and potential energy of its molecules. In the case of Refrigerant-134a, internal energy plays a significant role in determining how the refrigerant will act when it is compressed, expanded, or when it undergoes a phase change.

Knowing the internal energy of a refrigerant before and after a process, such as throttling, can provide insights into the state of the refrigerant, which is not always apparent from other properties. The relationship between internal energy and temperature is particularly important, as it can indicate phase changes and the refrigeration capacity of the substance.

Pressure-Temperature Relationship

The pressure-temperature relationship is a fundamental concept in thermodynamics that describes how the pressure of a substance correlates with its temperature, particularly when dealing with phase changes between the liquid and vapor states. For refrigerants like R-134a, this relationship is predictable and is characterized by its saturation curve.

In the given exercise, the throttling process results in a decrease in temperature without a change in enthalpy. By consulting the R-134a tables or diagrams, it's possible to determine the new saturation pressure at the final lower temperature, effectively solving for the refrigerant's final pressure which is crucial in designing refrigeration systems and for troubleshooting them when performance issues arise.