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Magazine Chapter 3: Problem 166
A cylinder fitted with a frictionless piston contains \(10 \mathrm{lbm}\) of superheated refrigerant R-134a vapor at \(100 \mathrm{lbf} / \mathrm{in} .{ }^{2}, 300 \mathrm{~F}\). The setup is cooled at constant pressure until the R-134a reaches a quality of \(50 \%\). Calculate the work done in the process.
Short Answer
Expert verified
The work done is the change in volume multiplied by constant pressure: \( W = P(V_2 - V_1) \).
Step by step solution
01
Understand the Problem
We have a cylinder containing superheated R-134a at a given pressure and temperature, and we need to find the work done as it cools to a specific quality, maintaining constant pressure.
02
Identify Initial and Final States
Initially, the refrigerant is superheated at 100 lbf/in虏 and 300掳F. The final state has the same pressure, but a quality of 50%, indicating a mixture of liquid and vapor.
03
Determine Initial and Final Specific Volumes
Using R-134a refrigerant tables, find the specific volume at the initial state (superheated condition) and the final state (saturated mixture at 50% quality).
04
Calculate Work Done with Constant Pressure Equation
For a constant pressure process, work done is given by \( W = P(V_2 - V_1) \), where \( V_1 \) and \( V_2 \) are initial and final volumes respectively. Multiply by specific volumes and mass to find total work.
05
Additional Task - Convert Units if Necessary
If the work is calculated in in鲁, convert it to a more convenient unit, like ft鲁, using the conversion factor (1 ft鲁 = 1728 in鲁), and ensure energy units are consistent. If using lbf-ft, convert from in-lbf accordingly.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Refrigerant R-134a
Refrigerant R-134a is a widely used refrigerant in various cooling and refrigeration systems. It is a type of hydrofluorocarbon (HFC), which is considered more environmentally friendly compared to older refrigerants like CFCs and HCFCs.
These older gases were phased out due to their damaging effects on the ozone layer. R-134a is non-toxic and has a lower ozone-depleting potential. When discussing its properties, R-134a is appreciated for its efficiency in heat transfer and its ability to operate under a wide range of temperatures. It is primarily used in automotive air conditioners, refrigerators, and larger industrial refrigeration systems. The reason R-134a is so effective in these applications is due to its specific thermodynamic properties.
These include its boiling point, critical temperature, and pressure, which allow it to absorb and release heat effectively during phase changes. Understanding these properties is crucial for calculating processes involving refrigerants, like the one in the provided exercise.
These older gases were phased out due to their damaging effects on the ozone layer. R-134a is non-toxic and has a lower ozone-depleting potential. When discussing its properties, R-134a is appreciated for its efficiency in heat transfer and its ability to operate under a wide range of temperatures. It is primarily used in automotive air conditioners, refrigerators, and larger industrial refrigeration systems. The reason R-134a is so effective in these applications is due to its specific thermodynamic properties.
These include its boiling point, critical temperature, and pressure, which allow it to absorb and release heat effectively during phase changes. Understanding these properties is crucial for calculating processes involving refrigerants, like the one in the provided exercise.
Specific Volume
Specific volume is a key concept in thermodynamics and refers to the volume occupied by a unit mass of a substance. This is particularly important for gases and liquids as it helps describe their physical state.
The specific volume is usually denoted as \(v\) and is generally measured in \( ext{ft}^3/ ext{lbm}\), or \( ext{m}^3/ ext{kg}\) in the metric system.In the context of refrigerant R-134a, specific volume is crucial to determine how the substance behaves under different conditions of temperature and pressure. In the exercise, we see the R-134a undergoing changes from a superheated vapor state to a mixture of liquid and vapor. To calculate the work done during this cooling process, we need to understand the change in specific volume as the refrigerant transitions between these states.
These values are typically sourced from specialized R-134a tables, where you can locate specific volumes at given temperatures and pressures. The ability to analyze and compute these changes allows engineers to design and manage cooling systems efficiently.
The specific volume is usually denoted as \(v\) and is generally measured in \( ext{ft}^3/ ext{lbm}\), or \( ext{m}^3/ ext{kg}\) in the metric system.In the context of refrigerant R-134a, specific volume is crucial to determine how the substance behaves under different conditions of temperature and pressure. In the exercise, we see the R-134a undergoing changes from a superheated vapor state to a mixture of liquid and vapor. To calculate the work done during this cooling process, we need to understand the change in specific volume as the refrigerant transitions between these states.
These values are typically sourced from specialized R-134a tables, where you can locate specific volumes at given temperatures and pressures. The ability to analyze and compute these changes allows engineers to design and manage cooling systems efficiently.
Work Done
Work done in thermodynamic processes often involves changes in volume at a given pressure. This makes understanding how to calculate it essential in various applications, especially within systems using substances like R-134a.
In general, the work done by or on a system during a process can be equated to the pressure times the change in volume. In this problem scenario, we are cooling refrigerant R-134a at a constant pressure, which simplifies the work calculation to the formula \( W = P(V_2 - V_1) \), where \( V_1 \) and \( V_2 \) are the specific volumes at the initial and final states.By calculating this work, we understand the energy transfer required during the cooling process. This is pivotal for effectively managing energy usage in refrigerating systems, ensuring both operational efficiency and environmental sustainability is maintained. Properly conveying this concept is crucial for students learning about thermodynamics and its practical applications.
In general, the work done by or on a system during a process can be equated to the pressure times the change in volume. In this problem scenario, we are cooling refrigerant R-134a at a constant pressure, which simplifies the work calculation to the formula \( W = P(V_2 - V_1) \), where \( V_1 \) and \( V_2 \) are the specific volumes at the initial and final states.By calculating this work, we understand the energy transfer required during the cooling process. This is pivotal for effectively managing energy usage in refrigerating systems, ensuring both operational efficiency and environmental sustainability is maintained. Properly conveying this concept is crucial for students learning about thermodynamics and its practical applications.
Cooling Process
The cooling process within thermodynamics typically involves removing heat from a substance, causing a decrease in temperature or a change in phase. In the context of R-134a, this cooling process is cleverly controlled to ensure efficiency and performance.
In this particular exercise, we start with superheated R-134a and cool it until it reaches a specific quality, which involves a precise change in its physical state. Quality refers to the ratio of the mass of vapor to the total mass of a liquid-vapor mixture. A 50% quality means the mixture is half liquid and half vapor. As the R-134a cools under constant pressure, the shift from superheated vapor to the mixture stage elaborates on the cooling dynamics at play.
Understanding these dynamics aids in mastering cooling cycles, pivotal to air conditioning, refrigeration, and even heat pumps. This knowledge can improve system designs, optimize energy consumption, and enhance environmental benefits, reinforcing why comprehending such topics fully is necessary for anyone studying thermodynamics.
In this particular exercise, we start with superheated R-134a and cool it until it reaches a specific quality, which involves a precise change in its physical state. Quality refers to the ratio of the mass of vapor to the total mass of a liquid-vapor mixture. A 50% quality means the mixture is half liquid and half vapor. As the R-134a cools under constant pressure, the shift from superheated vapor to the mixture stage elaborates on the cooling dynamics at play.
Understanding these dynamics aids in mastering cooling cycles, pivotal to air conditioning, refrigeration, and even heat pumps. This knowledge can improve system designs, optimize energy consumption, and enhance environmental benefits, reinforcing why comprehending such topics fully is necessary for anyone studying thermodynamics.
