Question

A piston-cylinder device contains 8 kg of refrigerant134a at \(0.7 \mathrm{MPa}\) and \(60^{\circ} \mathrm{C}\). The refrigerant is now cooled at constant pressure until it exists as a liquid at \(20^{\circ} \mathrm{C}\). If the surroundings are at \(100 \mathrm{kPa}\) and \(20^{\circ} \mathrm{C}\), determine (a) the exergy of the refrigerant at the initial and the final states and (b) the exergy destroyed during this process.

Short answer

Based on the given information, calculate the initial and final exergy of the refrigerant and the exergy destroyed during the process.

Step-by-step solution

Determine the specific properties at the initial state

Using the refrigerant 134a tables and locating the given parameters (0.7MPa and 60°C), find the initial specific internal energy (\(u_1\)), specific enthalpy (\(h_1\)), and specific entropy (\(s_1\)). Mark this as state 1.

Determine the specific properties at the final state

Using the refrigerant 134a tables and locating the given parameters (0.7MPa and 20°C), find the final specific internal energy (\(u_2\)), specific enthalpy (\(h_2\)), and specific entropy (\(s_2\)). Mark this as state 2.

Calculate the initial and final exergy

The exergy at a given state is calculated as: Exergy = mass × [(initial specific internal energy - final specific internal energy) - T0 × (initial specific entropy - final specific entropy) + P0 × (initial specific volume - final specific volume)] Use this formula to find the initial and final exergy by substituting the identified values of specific properties and the given mass, environmental temperature (T0 = 20°C = 293.15K), and environmental pressure (P0 = 100 kPa).

Calculate the exergy destroyed

Exergy destroyed can be calculated using the following formula: Exergy destroyed = Exergy of the refrigerant at the final state - Exergy of the refrigerant at the initial state Plug in the values of initial and final exergy that you calculated in Step 3 to find the exergy destroyed during this process.

Key concepts

Understanding Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In essence, it looks at how thermal energy is converted to and from other forms of energy and how it affects matter. The first law of thermodynamics states that energy can neither be created nor destroyed, only transferred or transformed. This principle is known as the conservation of energy. In the context of our exercise involving a piston-cylinder device containing refrigerant-134a, thermodynamics guides us on how energy is transferred during the cooling process.

When a refrigerant is cooled, it undergoes a phase change from a gaseous state to a liquid state while releasing energy in the form of heat. This heat transfer is an example of a thermodynamic process. By applying the laws of thermodynamics, we can calculate various properties of the refrigerant and analyze energy transfer, which is crucial for the understanding of cooling systems in engineering applications.

Refrigerant Properties

Refrigerants play a central role in refrigeration cycles. They are substances used in a closed cycle to absorb heat, transport it away, and release the heat at a different location. Refrigerant-134a, mentioned in the exercise, is a common type of refrigerant used in HVAC (Heating, Ventilation, and Air Conditioning) applications. Its properties change significantly with pressure and temperature; thus, exact values are found in refrigerant tables, which are used heavily in thermodynamic calculations.

To perform an exergy analysis, we require the specific internal energy (\(u\)), enthalpy (\(h\)), and entropy (\(s\)) of the refrigerant in various states. These thermodynamic properties can help us determine the amount of work that can be extracted from a refrigeration cycle and allow us to optimize the system. Knowing the initial and final states of the refrigerant, as given in the exercise, allows us to calculate the exergy, which is a measure of the work potential in a system.

Exergy Destruction

Exergy destruction is an important concept within the second law of thermodynamics, which is concerned with the directions of processes and the conversion of energy into work. It reflects the loss of potential work due to irreversibilities in a thermodynamic system. Exergy destruction is associated with inefficiencies such as friction, mixing, chemical reactions, and heat loss.

The idea of exergy destruction is central to understanding efficiency and sustainability in engineering systems. During our exercise's cooling process, exergy destruction is calculated by finding the difference between the exergy at the final state and the initial state of the refrigerant. Any decrease in exergy signifies a lessening of the system's ability to perform work, which corresponds to energy degradation—a key insight when looking to optimize thermal systems for minimal waste and maximum efficiency.