The Physics
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Opus in profectus

Refrigerators

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Problems

practice

  1. A manufacturer tested a window-mounted, residential heat pump and reported the following results.

    Testing a window-mounted, residential heat pump
    heating mode cooling mode both modes
    heating capacity
    7.9 MJ/hour    		 cooling capacity
    10 MJ/hour    		  
    heating amps
    7.6 amps    		 cooling amps
    7.8 amps    		 volts rated
    115 volts
    heating watts
    743 watts    		 cooling watts
    812 watts    		 air circulation
    8.1 m3/minute
    outdoor air
    temperature
    17 °C    		 outdoor air
    temperature
    35 °C    		 width
    66 cm
    indoor air
    temperature
    21 °C    		 indoor air
    temperature
    27 °C    		 height
    40 cm
      moisture removal
    0.9 liter/hour    		 depth
    74 cm

    Using this information and your knowledge of physics, determine…

    1. the heat…
      1. extracted from the environment per hour when the device is operated in heating mode
      2. exhausted to the environment per hour when the device is operated in cooling mode
    2. the real coefficient of performance for the heat pump…
      1. in heating mode
      2. in cooling mode
    3. the ideal coefficient of performance for the heat pump…
      1. in heating mode
      2. in cooling mode

    Not only does a heat pump transfer heat into or out of a house, it also circulates the air inside.

    1. Determine the velocity of the air blowing out of the heat pump tested above when operated in either mode.

    Not only can a heat pump transfer heat into or out of a house it can also dehumidify the air inside when operated in cooling mode.

    1. Determine the following quantities for the heat pump tested above if it is both cooling and dehumidifying the air inside a house at its rated capacity…
      1. the latent heat extracted from inside the house per hour
      2. the new heat exhausted to the environment per hour
      3. the new real coefficient of performance
  2. Write something else.
  3. Write something different.
  4. Write something completely different.

numerical

  1. One millimole of a monatomic, ideal gas is run through a four-step cycle as shown in the table below.
    1. Sketch the cycle on a PV graph.
    2. Determine the absolute temperature of the gas when it is in states A, B, C, and D.
    3. Determine ΔU, Q, and W for each segment of the cycle (A→B, B→C, C→D, D→A) and for the cycle as a whole (ABCDA). Include an algebraic sign with each answer. (Zero values do not get a sign.)
    4. Determine the real coefficient of performance assuming the cycle is used as a refrigerator.
    5. Determine the ideal coefficient of performance for this refrigerator.
    6. How are the answers to the last two questions in apparent conflict? Why are they?
    A four step closed cycle
    state A B C D
    P (kPa) 100 624 312 100  
    V (m3) 24 × 10−6 8 × 10−6 8 × 10−6 16 × 10−6  
    T (K)          
    path A→B B→C C→D D→A ABCA
    descrip­tion adia­batic iso­choric adia­batic iso­baric whole cycle
    ∆U (J)          
    Q (J)          
    W (J)