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Chapter 7: Problem 56

Refrigerant \(134 \mathrm{a}\) at \(100 \mathrm{lb} / \mathrm{in} .^{2}, 200^{\circ} \mathrm{F}\) enters a valve operating at steady state and undergoes a throttling process. (a) Determine the exit temperature, in \({ }^{\circ} F\), and the exergy destruction rate, in Btu per lb of Refrigerant 134a flowing, for an exit pressure of \(50 \mathrm{lbf} / \mathrm{in}^{2}\). \(^{2}\) (b) Plot the exit temperature, in \({ }^{\circ} \mathrm{F}\), and the exergy destruction rate, in Btu per lb of Refrigerant 134a flowing, each versus exit pressure ranging from 50 to \(100 \mathrm{lbf} /\) in. \({ }^{2}\) Let \(T_{0}=70^{\circ} \mathrm{F}, p_{0}=14.7 \mathrm{lbf} / \mathrm{in}^{2}{ }^{2}\)

Short Answer

Expert verified
Exit temperature is obtained by keeping enthalpy constant during throttling. Exergy destruction is determined using the Gouy-Stodola theorem.

Step by step solution

01

Identify Initial State Properties

Identify the properties of Refrigerant 134a at the initial state (entrance of the valve): pressure is 100 lbf/in^2 and temperature is 200掳F. Using the Refrigerant 134a tables or a software like REFPROP, find the corresponding specific enthalpy, h1.
02

Apply the Throttling Process

In a throttling process, the enthalpy remains constant. Therefore, the specific enthalpy at the exit, h2, is equal to h1. Use the known exit pressure of 50 lbf/in^2 and the specific enthalpy h2 to find the exit temperature T2 from Refrigerant 134a tables or REFPROP.
03

Calculate Exergy Destruction

Use the given ambient conditions (T0 = 70掳F, p0 = 14.7 lbf/in^2) to calculate the exergy destruction. The exergy destruction rate per lb of Refrigerant 134a flowing through the valve can be found using the Gouy-Stodola theorem for throttling processes: \( \text{Exergy Destruction} = T_{0} \times (s_2 - s_1) \) Where T0 is the ambient temperature in Rankine (convert 70掳F to Rankine), s1 is the specific entropy at the inlet, and s2 is the specific entropy at the outlet.
04

Plot the Exit Temperature and Exergy Destruction

For part (b), repeat the calculations from steps 1, 2, and 3 for different exit pressures ranging from 50 to 100 lbf/in^2. Plot the resulting exit temperatures and exergy destruction rates against the exit pressures to visualize the relationships.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Throttling Process
In refrigeration systems, the throttling process is a key operation. It involves the expansion of refrigerant from a high-pressure region to a low-pressure region without any heat exchange or work being performed. Essentially, the refrigerant passes through a valve, and during this process, its enthalpy remains constant. That means the energy content before and after the valve does not change.
What does change, however, is the pressure and temperature of the refrigerant. The drop in pressure results in a corresponding drop in temperature. This process is fundamental because it helps us achieve the desired cooling effect by lowering the temperature of the refrigerant before it enters the evaporator.
Refrigerant Properties
Refrigerant 134a, also known as R-134a, is a common refrigerant used in various cooling and refrigeration systems. It possesses specific properties that make it suitable for such applications, including its non-flammability and relatively low toxicity.
Key properties to consider are:
  • Pressure and Temperature: These are crucial because they determine the state of the refrigerant (liquid or gas).
  • Specific Enthalpy (h): Represents the total energy per unit mass, significant in analyzing thermodynamic processes.
  • Specific Entropy (s): Important for understanding the thermal disorder and exergy calculations.
Knowing these properties at various states (before and after throttling) helps in analyzing and defining the performance and efficiency of cooling cycles.
Exergy Analysis
Exergy analysis focuses on evaluating the quality of energy within a system. In thermodynamics, exergy is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir. For a throttling process, the exergy destruction can be evaluated using the Gouy-Stodola theorem:
\( \text{Exergy Destruction} = T_{0} \times (s_2 - s_1) \)
Here, \( T_{0} \) is the ambient temperature in Rankine, \( s_1 \) is the specific entropy at the initial state, and \( s_2 \) is the specific entropy at the final state. Higher exergy destruction rates indicate higher inefficiencies in the system. This analysis helps to improve the design and operation of refrigeration processes by minimizing losses.
Entropy in Thermodynamics
Entropy is a fundamental concept in thermodynamics, representing the degree of disorder or randomness in a system and the unavailability of a system鈥檚 energy to do work. In the context of refrigeration cycles, understanding entropy changes is crucial because it affects the efficiency of the process.
For a throttling process, the entropy of the refrigerant will increase due to irreversibilities and the lack of heat exchange or work input. Using specific entropy values from tables or software tools like REFPROP at different states (before and after throttling) allows us to calculate the entropy change:
\( \text{Entropy Change} = s_2 - s_1 \)
This change is essential for determining the exergy destruction rate and thus the efficiency of the refrigeration process. By understanding and managing entropy, engineers can design more effective cooling systems.

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Most popular questions from this chapter

When matter flows across the boundary of a control volume, an energy transfer by work, called flow work, occurs. The rate is \(\dot{m}(p v)\) where \(\dot{m}, p\), and \(v\) denote the mass flow rate, pressure, and specific volume, respectively, of the matter crossing the boundary (see Sec. 4.4.2). Show that the exergy transfer accompanying flow work is given by \(\dot{m}\left(p v-p_{0} v\right)\), where \(p_{0}\) is the pressure at the dead state.

Nitrogen \(\left(\mathrm{N}_{2}\right)\) at 25 bar, \(450 \mathrm{~K}\) enters a turbine and expands to \(2 \mathrm{bar}, 250 \mathrm{~K}\) with a mass flow rate of \(0.2 \mathrm{~kg} / \mathrm{s}\) The turbine operates at steady state with negligible heat transfer with its surroundings. Assuming the ideal gas model with \(k=\) \(1.399\) and ignoring the effects of motion and gravity, determine (a) the isentropic turbine efficiency. (b) the exergetic turbine efficiency. Let \(T_{0}=25^{\circ} \mathrm{C}, p_{0}=1 \mathrm{~atm}\).

Steam at \(200 \mathrm{lbf} / \mathrm{in}^{2}, 660^{\circ} \mathrm{F}\) enters a turbine operating at steady state with a mass flow rate of \(16.5 \mathrm{lb} / \mathrm{min}\) and exits at 14.7 lbffin. \({ }^{2}, 238^{\circ}\) F. Stray heat transfer and the effects of motion and gravity can be ignored. Let \(T_{0}=537^{\circ} \mathrm{R}, p_{0}=14.7 \mathrm{lbf} / \mathrm{in}^{2}{ }^{2}\) Determine for the turbine (a) the power developed and the rate of exergy destruction, each in Btu/min, and (b) the isentropic and exergetic turbine efficiencies.

Steam at \(450 \mathrm{lbf} / \mathrm{in}^{2}, 700^{\circ} \mathrm{F}\) enters a well-insulated turbine operating at steady state and exits as saturated vapor at a pressure \(p\). (a) For \(p=50 \mathrm{lbf} / \mathrm{in}^{2}{ }^{2}\), determine the exergy destruction rate, in Btu per lb of steam expanding through the turbine, and the turbine exergetic and isentropic efficiencies. (b) Plot the exergy destruction rate, in Btu per lb of steam flowing, and the exergetic efficiency and isentropic efficiency, each versus pressure \(p\) ranging from 1 to \(50 \mathrm{lbf} / \mathrm{in}^{2}{ }^{2}\) Ignore the effects of motion and gravity and let \(T_{0}=70^{\circ} \mathrm{F}\), \(p_{0}=1 \mathrm{~atm} .\)

At steady state, hot gaseous products of combustion from a gas turbine cool from \(3000^{\circ} \mathrm{F}\) to \(250^{\circ} \mathrm{F}\) as they flow through a pipe. Owing to negligible fluid friction, the flow occurs at nearly constant pressure. Applying the ideal gas model with \(c_{p}=0.3 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), determine the exergy transfer accompanying heat transfer from the gas, in Btu per lb of gas flowing. Let \(T_{0}=80^{\circ} \mathrm{F}\) and ignore the effects of motion and gravity.
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