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Chapter 11: Problem 53

A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1.4 and 0.10 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The refrigerant leaving the low-pressure compressor at \(0.4 \mathrm{MPa}\) is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine ( \(a\) ) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, ( \(b\) ) the rate of heat removed from the refrigerated space for a mass flow rate of \(0.25 \mathrm{kg} / \mathrm{s}\) through the condenser, and ( \(c\) ) the coefficient of performance.

Short Answer

Expert verified
Question: In a two-stage compression refrigeration system using refrigerant-134a, with pressure limits of \(P_1 = 0.1 \,\mathrm{MPa}, P_2 = P_4 = 0.4 \,\mathrm{MPa}, P_3 = P_5 = 1.4 \,\mathrm{MPa}\), and a mass flow rate of 0.25 kg/s through the condenser, calculate (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space, and (c) the coefficient of performance of the refrigeration system. Answer: (a) The fraction of the refrigerant that evaporates (x) can be calculated as: \(x = \frac{h_5 - h_1}{h_4 - h_1}\) (b) The rate of heat removed from the refrigerated space (Q_evap) can be calculated as: \(Q_{evap} = m_{cond}(h_1 - h_{5s})\) (c) The coefficient of performance (COP) can be calculated as: \(COP = \frac{Q_{evap}}{W_{comp1} + W_{comp2}}\) Note: The specific enthalpies and entropies needed for these calculations can be found in the Refrigerant-134a Property Tables.

Step by step solution

01

Determine the Properties of Refrigerant at Different Points in the Cycle

First, we need to find the specific enthalpies (h) and specific entropies (s) for the refrigerant at different points throughout the cycle using the given pressures, i.e., \(P_1 = 0.1 \,\mathrm{MPa}, P_2 = P_4 = 0.4 \,\mathrm{MPa}, P_3 = P_5 = 1.4 \,\mathrm{MPa}\). Refer to the Refrigerant-134a Property Tables to find the specific enthalpies and entropies at these respective pressures and for the given conditions (e.g., saturated liquid, saturated vapor, etc.).
02

Calculate the Fraction of Refrigerant that Evaporates (x)

We have determined the specific enthalpies (h) and specific entropies (s) for \(s_1 = s_2 = s_3\) and \(h_1, h_2, h_3, h_4, h_5\). Now we can calculate the fraction of refrigerant that evaporates as it is throttled to the flash chamber. Use the following formula: \(x = \frac{h_5 - h_1}{h_4 - h_1}\) Calculate the value of x using the values of h found in Step 1.
03

Calculate the Rate of Heat Removed (Q_evap)

Now, find the rate of heat removed from the refrigerated space. Use the mass flow rate \(m_{cond} = 0.25 \,\mathrm{kg/s}\) and the enthalpy difference across the evaporator. The formula for finding the rate of heat removed is: \(Q_{evap} = m_{cond}(h_1 - h_{5s})\) Calculate the value for \(Q_{evap}\) using the values found in Step 1 and the given mass flow rate.
04

Calculate the Coefficient of Performance (COP)

Finally, we need to find the coefficient of performance (COP) of the refrigeration system. We first need to find the values of \(W_{comp1}\) and \(W_{comp2}\), which are the work done by the low-pressure and high-pressure compressors, respectively. \(W_{comp1}\) = \((1-x)m_{cond}(h_2 - h_1)\) \(W_{comp2}\) = \(m_{cond}(h_3 - h_4)\) Now, we can find the COP: \(COP = \frac{Q_{evap}}{W_{comp1} + W_{comp2}}\) Calculate the value of COP using the values found in Steps 3, and the work values calculated above. Now, we have determined (a) the fraction of the refrigerant that evaporates during throttling to the flash chamber, (b) the rate of heat removed from the refrigerated space, and (c) the coefficient of performance for this two-stage compression refrigeration system.

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Most popular questions from this chapter

Refrigerant- 134 a enters the compressor of a refrigerator at \(100 \mathrm{kPa}\) and \(-20^{\circ} \mathrm{C}\) at a rate of \(0.5 \mathrm{m}^{3} / \mathrm{min}\) and leaves at 0.8 MPa. The isentropic efficiency of the compressor is 78 percent. The refrigerant enters the throttling valve at \(0.75 \mathrm{MPa}\) and \(26^{\circ} \mathrm{C}\) and leaves the evaporator as saturated vapor at \(-26^{\circ} \mathrm{C}\). Show the cycle on a \(T\) -s diagram with respect to saturation lines, and determine ( \(a\) ) the power input to the compressor, \((b)\) the rate of heat removal from the refrigerated space, and ( \(c\) ) the pressure drop and rate of heat gain in the line between the evaporator and the compressor.

A refrigeration unit operates on the ideal vapor compression refrigeration cycle and uses refrigerant-22 as the working fluid. The operating conditions for this unit are evaporator saturation temperature of \(-5^{\circ} \mathrm{C}\) and the condenser saturation temperature of \(45^{\circ} \mathrm{C}\). Selected data for refrigerant- 22 are provided in the table below. $$\begin{array}{lcccc}\hline T,^{\circ} \mathrm{C} & P_{\text {sat }}, \mathrm{kPa} & h_{f}, \mathrm{kJ} / \mathrm{kg} & h_{g}, \mathrm{kJ} / \mathrm{kg} & s_{g}, \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K} \\ \hline-5 & 421.2 & 38.76 & 248.1 & 0.9344 \\\45 & 1728 & 101 & 261.9 & 0.8682 \\\\\hline\end{array}$$ For \(R-22\) at \(P=1728\) kPa and \(s=0.9344 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) \(T=68.15^{\circ} \mathrm{C}\) and \(h=283.7 \quad \mathrm{kJ} / \mathrm{kg} .\) Also, take \(c_{p, \text { air }}=1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) (a) Sketch the hardware and the \(T\) -s diagram for this heat pump application. (b) Determine the COP for this refrigeration unit. (c) The evaporator of this unit is located inside the air handler of the building. The air flowing through the air handler enters the air handler at \(27^{\circ} \mathrm{C}\) and is limited to a \(20^{\circ} \mathrm{C}\) temperature drop. Determine the ratio of volume flow rate of air entering the air handler \(\left(m_{\text {ail }}^{3} / \min \right)\) to mass flow rate of \(\mathrm{R}-22\left(\mathrm{kg}_{\mathrm{R}-22} / \mathrm{s}\right)\) through the air handler, in \(\left(m_{\mathrm{air}}^{3} / \mathrm{min}\right) /\left(\mathrm{kg}_{\mathrm{R}-22} / \mathrm{s}\right) .\) Assume the air pressure is \(100 \mathrm{kPa}\).

Design a thermoelectric refrigerator that is capable of cooling a canned drink in a car. The refrigerator is to be powered by the cigarette lighter of the car. Draw a sketch of your design. Semiconductor components for building thermoelectric power generators or refrigerators are available from several manufacturers. Using data from one of these manufacturers, determine how many of these components you need in your design, and estimate the coefficient of performance of your system. A critical problem in the design of thermoelectric refrigerators is the effective rejection of waste heat. Discuss how you can enhance the rate of heat rejection without using any devices with moving parts such as a fan.

Using EES (or other) software, investigate the effect of the evaporator pressure on the COP of an ideal vapor-compression refrigeration cycle with \(\mathrm{R}-134 \mathrm{a}\) as the working fluid. Assume the condenser pressure is kept constant at \(1.4 \mathrm{MPa}\) while the evaporator pressure is varied from \(100 \mathrm{kPa}\) to \(500 \mathrm{kPa}\). Plot the COP of the refrigeration cycle against the evaporator pressure, and discuss the results.

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at \(0.20 \mathrm{MPa}\) and \(-5^{\circ} \mathrm{C}\) at a rate of \(0.07 \mathrm{kg} / \mathrm{s},\) and it leaves at \(1.2 \mathrm{MPa}\) and \(70^{\circ} \mathrm{C}\). The refrigerant is cooled in the condenser to \(44^{\circ} \mathrm{C}\) and \(1.15 \mathrm{MPa}\), and it is throttled to 0.21 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, show the cycle on a \(T\) -s diagram with respect to saturation lines, and determine ( \(a\) ) the rate of heat removal from the refrigerated space and the power input to the compressor, \((b)\) the isentropic efficiency of the compressor, and \((c)\) the \(C O P\) of the refrigerator.
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