Question

How much exergy is lost in a rigid vessel filled with 1 kg of liquid \(R-134\) a, whose temperature remains constant at \(24^{\circ} \mathrm{C},\) as \(\mathrm{R}-134 \mathrm{a}\) vapor is released from the vessel? This vessel may exchange heat with the surrounding atmosphere, which is at \(100 \mathrm{kPa}\) and \(24^{\circ} \mathrm{C}\). The vapor is released until the last of the liquid inside the vessel disappears.

Short answer

Answer: To calculate the exergy loss in this process, you need to follow these steps: 1. Identify the initial and final states of the R-134a. 2. Find the specific enthalpy and specific entropy values at these states using R-134a saturation table. 3. Calculate the heat transfer during the process using the specific enthalpies. 4. Calculate the entropy change during the process using the specific entropies. 5. Calculate the exergy loss using the formula: ΔEx = m⋅T₀⋅ΔS - Q. Note: To give a numerical value for the exergy loss, you need to refer to the R-134a saturation table to find the specific enthalpy and entropy values at the initial and final states.

Step-by-step solution

Identify the initial state of the R-134a

First, we need to find the initial state of R-134a which is a liquid at \(24^{\circ} \mathrm{C}\). We can refer to the R-134a saturation table to find the specific enthalpy and specific entropy at this temperature in the liquid phase.

Identify the final state of the R-134a

As the R-134a vapor is released from the vessel, the last of the liquid R-134a disappears. At this state, the R-134a is a saturated vapor at \(24^{\circ} \mathrm{C}\). We can find the specific enthalpy and specific entropy at this final state from the R-134a saturation table.

Calculate the heat transfer during the process

Since the temperature of the R-134a remains constant during the entire process, we can use the specific enthalpies at the initial and final states to calculate the heat transfer in the process. The formula for heat transfer, \(Q\), in a constant temperature process is: $$Q = m \cdot (h_f - h_i)$$ where \(m\) is the mass of the R-134a (1 kg), \(h_i\) and \(h_f\) are the specific enthalpies at the initial and final states, respectively.

Calculate the entropy change during the process

Using the specific entropies at the initial and final states, we can calculate the entropy change (\(\Delta S\)) during the process. $$\Delta S = m \cdot (s_f - s_i)$$ where \(s_i\) and \(s_f\) are the specific entropies at the initial and final states, respectively.

Calculate the exergy loss during the process

The exergy loss in the process is given by the following equation: $$\Delta Ex = m \cdot T_0 \cdot \Delta S - Q$$ where \(T_0\) is the surrounding temperature at \(24^{\circ} \mathrm{C} = 297.15 \mathrm{K}\). We can now use the values obtained from steps 3 and 4 to calculate the exergy loss in this process. Using all the information and steps above, we can calculate the exergy loss in the process when R-134a vapor is released from the vessel until the last of the liquid disappears.

Key concepts

R-134a Thermodynamic Properties

Refrigerant-134a, also known as R-134a, is commonly used in refrigeration and air conditioning systems. The thermodynamic properties of R-134a include its pressure, temperature, specific volume, specific enthalpy, and specific entropy, which vary depending on whether the substance is in the liquid or vapor phase.

For engineers and students working in the field of thermodynamics, it is essential to understand these properties to predict how R-134a will behave under different conditions. Accurate values can typically be found in R-134a refrigerant tables or calculated using equations of state. Knowing its thermodynamic properties enables practitioners to design systems efficiently, ensuring that the application, whether it's a refrigerator or a heat pump, operates optimally.

Entropy Change

Entropy change is a fundamental concept in thermodynamics representing the measure of disorder or randomness in a system. It's a crucial variable when analyzing energy conversions and transfers, such as in the process described in the exercise. When a system undergoes a change, such as the R-134a in the rigid vessel transitioning from liquid to vapor, the entropy change can be determined.

Computing the difference in specific entropy between the final and initial states helps quantify this change. An increase in entropy typically indicates that energy has been spread out within the system or transferred to the surroundings, often resulting in exergy loss, which measures the usefulness of energy in a process.

Heat Transfer Thermodynamics

Heat transfer in thermodynamics refers to the movement of thermal energy from one place to another. It's driven by temperature differences and occurs via three main mechanisms: conduction, convection, and radiation.

In the case of a constant temperature process as described in our exercise, the concept of isothermal heat transfer comes into play. The amount of heat transferred can be determined from the change in specific enthalpy, allowing for the calculation of energy that flows out of the rigid vessel. This is essential for the calculation of exergy loss, which measures the maximum work potential of a thermodynamic system as it moves towards equilibrium with its environment.

Saturated Vapor

A saturated vapor occurs when a substance is at a temperature and pressure where vapor and liquid phases can coexist in equilibrium. At this point, the vapor is at its dew point, and any addition of thermal energy will result in a phase change to entirely vapor without a change in temperature.

In our problem, R-134a reaches a state of saturated vapor when the last of the liquid in the vessel disappears. This specific state is important for calculations because the thermodynamic properties of saturated vapor are used to determine entropy and enthalpy values at the final state, which are needed for exergy loss calculations.

Specific Enthalpy

Specific enthalpy is the total enthalpy per unit mass of a substance and denotes the energy content within that substance. It is a combination of the substance's internal energy and the work done by the substance in pushing the surrounding atmosphere to make space for itself.

Knowing the specific enthalpies at the beginning and end of a thermodynamic process enables one to calculate the amount of heat transfer that has occurred, as outlined in the step-by-step solution of the exercise. The importance of accurate specific enthalpy values cannot be overstated, as they directly impact the analysis and understanding of energy transformations and, consequently, the determination of system efficiency and exergy loss.

Specific Entropy

Specific entropy, a measure of disorder at the molecular level per unit mass, is another key thermodynamic property that quantifies the randomness or chaos in a system. This property offers insight into the irreversibility of a process and is used along with specific enthalpy to determine the direction and magnitude of energy transformations.

In a process where R-134a transitions from liquid to saturated vapor, the specific entropy increases, reflecting the growing disorder as the substance moves from a more structured liquid state to a less structured gaseous state. This change in specific entropy, highlighted in the solved exercise, is essential for calculating both the energy absorbed or released during a process and the associated exergy loss.