{"id":1832,"date":"2021-07-27T20:21:56","date_gmt":"2021-07-28T00:21:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/thermo1\/chapter\/6-2-refrigerator-and-heat-pump\/"},"modified":"2022-08-11T17:49:34","modified_gmt":"2022-08-11T21:49:34","slug":"6-2-refrigerator-and-heat-pump","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/thermo1\/chapter\/6-2-refrigerator-and-heat-pump\/","title":{"raw":"6.2 Refrigerator and heat pump","rendered":"6.2 Refrigerator and heat pump"},"content":{"raw":"
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6.2.1 Refrigerator<\/h2>\r\nA refrigerator is a cyclic device, which absorbs heat from a [pb_glossary id=\"2428\"]heat sink[\/pb_glossary] and reject heat to a [pb_glossary id=\"2427\"]heat source[\/pb_glossary] by consuming work. The working fluid is called refrigerant, which usually undergoes phase changes in the cycle.\r\n\r\n \r\n

A typical vapour-compression refrigeration system consists of mainly four pieces of equipment, as shown in Figure 6.2.1<\/a>:<\/p>\r\n\r\n

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  1. An evaporator, through which the low-pressure, low-temperature refrigerant absorbs heat from a heat sink (e.g., a freezer compartment or a space to be refrigerated) and changes from a two-phase mixture to a saturated or superheated vapour.<\/li>\r\n \t
  2. A compressor, which is used to increase the pressure and temperature of the refrigerant vapour by consuming work.<\/li>\r\n \t
  3. A condenser, through which heat is rejected to a heat source (e.g. kitchen or outdoor air). At the exit of the condenser, the refrigerant is typically a two-phase mixture or a liquid.<\/li>\r\n \t
  4. An expansion valve, which is used to reduce the pressure and temperature of the refrigerant in order to achieve a liquid-vapour mixture of desirable quality at the exit of the expansion <\/a>valve.<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_2665\" align=\"aligncenter\" width=\"500\"]\"Vapor<\/a> Figure 6.2.1<\/strong><\/em>\u00a0Vapor compression refrigeration cycle consisting of a compressor, condenser, expansion device, and evaporator<\/em>[\/caption]\r\n

    As heat cannot be transferred from a low-temperature body to a high-temperature body spontaneously in nature, refrigerators must consume work<\/em> in order to operate between a [pb_glossary id=\"2428\"]heat sink[\/pb_glossary] and a [pb_glossary id=\"2427\"]heat source[\/pb_glossary], even under ideal conditions.<\/p>\r\n \r\n\r\nFigure 6.2.2<\/a> is a schematic for analyzing the energy conservation in a refrigerator. The same schematic may be used to represent a heat pump by replacing the notation \u201cRef\u201d with \u201cHP\u201d in the circular <\/a>area.\r\n\r\n \r\n\r\n<\/div>\r\n\r\n[caption id=\"attachment_3513\" align=\"aligncenter\" width=\"238\"]\"Schematic<\/a> Figure 6.2.2<\/strong> Schematic of a refrigerator (or a heat pump)<\/em>[\/caption]\r\n

    Applying the first law of thermodynamics to the cycle, we can write<\/p>\r\n \r\n

    [latex]{\\dot{Q}}_H-{\\dot{Q}}_L = {\\dot{W}}_{in}[\/latex]<\/p>\r\n \r\n

    The main purpose of refrigerators is to remove heat, [latex]\\dot{Q}_L[\/latex], from a [pb_glossary id=\"2428\"]heat sink[\/pb_glossary] (cold space); therefore, we are interested in the amount of heat that can be removed per unit of power consumption. The dimensionless ratio of [latex]\\dot{Q}_L\/{\\dot{W}}_{in} [\/latex]\u00a0 is called the coefficient of performance, [latex]{COP}_R[\/latex], of the refrigerator. It is an indicator of the performance of a refrigerator.<\/p>\r\n

    [latex]{COP}_R=\\displaystyle\\frac{desired\\ output}{required\\ input}=\\frac{{\\dot{Q}}_L}{{\\dot{W}}_{in}}=\\frac{{\\dot{Q}}_L}{{\\dot{Q}}_H-{\\dot{Q}}_L}=\\frac{1}{{\\dot{Q}}_H\/{\\dot{Q}}_L-1}[\/latex]<\/p>\r\n \r\n\r\nRefrigerators are typically designed to consume a power [latex]{\\dot{W}}_{in}<{\\dot{Q}}_L[\/latex]; therefore, [latex]COP_R > 1[\/latex] in a well-designed refrigerator. A higher [latex]{COP}_R[\/latex] indicates a better performance.\r\n

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    6.2.2 Heat pump<\/h2>\r\nA heat pump uses the same vapour compression refrigeration cycle, see Figure 6.2.1<\/a>, as a refrigerator. It absorbs heat from a [pb_glossary id=\"2428\"]heat sink[\/pb_glossary] (e.g., outdoor air in the winter) and delivers (more) heat to a [pb_glossary id=\"2427\"]heat source[\/pb_glossary] (e.g., indoor air) by consuming work.\u00a0 Applying the first law of thermodynamics to the heat pump cycle, we can derive\r\n

    [latex]{\\dot{W}}_{in}={\\dot{Q}}_H-{\\dot{Q}}_L[\/latex]<\/p>\r\n \r\n\r\nDifferent from refrigerators, the main purpose of heat pumps is to add heat, [latex]{\\dot{Q}}_H[\/latex], to a heat source, such as an indoor space of a building. Therefore, we are interested in the amount of heat, [latex]{\\dot{Q}}_H[\/latex], that can be transferred from the condenser to the heat source per unit power consumption. The dimensionless ratio of [latex]\\dot{Q}_H\/{\\dot{W}}_{in} [\/latex] is called the coefficient of performance, [latex]{COP}_{HP}[\/latex], of heat pump. It is an indicator of the performance of a heat pump. As [latex]{\\dot{Q}_H} > {\\dot{W}}_{in}[\/latex], [latex]{COP}_{HP} > 1[\/latex].\r\n\r\n \r\n

    [latex]{COP}_{HP}=\\displaystyle\\frac{desired\\ output}{required\\ input}=\\frac{{\\dot{Q}}_H}{{\\dot{W}}_{in}}=\\frac{{\\dot{Q}}_H}{{\\dot{Q}}_H-{\\dot{Q}}_L}=\\frac{\\dot{Q}_H\/{\\dot{Q}}_L}{\\dot{Q}_H\/{\\dot{Q}}_L-1}[\/latex]<\/p>\r\n \r\n\r\n<\/div>\r\n

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    Example 1<\/p>\r\n\r\n<\/header>\r\n

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    Consider a vapour-compression refrigeration cycle, Figure 6.2.1<\/a>. The working fluid is ammonia.<\/p>\r\n\r\n