An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 ∘ C and rejects heat to a room at a temperature of 22.5 ∘ C. Suppose that liquid water with a mass of 85.7 kg at 0.0 ∘ C is converted to ice at the same temperature. Take the heat of fusion for water to be L f = 3.34 × 105 J / k g .How much energy E must be supplied to the device?

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An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at       0.0    ∘    C and rejects heat to a room at a temperature of       22.5    ∘    C. Suppose that liquid water with a mass of 85.7 kg at       0.0    ∘    C is converted to ice at the same temperature. Take the heat of fusion for water to be   L  f  =  3.34  ×  105  J      /    k  g .How much energy E must be supplied to the device?

plenarnoDcg · Accepted Answer

The amount of energy that must be supplied to the device is calculated using the opposite principle of a heat engine. The value obtained is   2  ,  359  ,  104.39  J  .Refrigerator and Carnot EngineGiven that cooler temperature is,      T    1    =      0    ∘    C  =  273  KThe hotter temperature is;      T    2    =      22.5    ∘    C  =  295.5  KThe heat used to melt a certain mass of water can be given as;      Q    1    =  m  ×      L    f  Substituting the known values, we get;      Q    1    =  85.7  k  g  ×  3.34  ×      10    5    J      /    k  g  =  28623800  JNow, we use the Carnot engine equation, we get;Therefore,      Q    2    =                    Q        1                    T        2                    T      2        =            28623800      J      ×      295.5      K              273      K        =  30982904.39  JThe work on the refrigerator is given by;  W  =      Q    2    −      Q    1    =  30982904.39  J  −  28623800  J  =  2359104.39  JHence the energy that must be applied is   E  =  2359104.39  J

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