It is often stated that the refrigerator door should be opened as few times as
possible for the shortest duration of time to save energy. Consider a
household refrigerator whose interior volume is \(0.9 \mathrm{m}^{3}\) and
average internal temperature is \(4^{\circ} \mathrm{C} .\) At any given time,
one-third of the refrigerated space is occupied by food items, and the
remaining \(0.6 \mathrm{m}^{3}\) is filled with air. The average temperature and
pressure in the kitchen are \(20^{\circ} \mathrm{C}\) and \(95 \mathrm{kPa}\),
respectively. Also, the moisture contents of the air in the kitchen and the
refrigerator are 0.010 and \(0.004 \mathrm{kg}\) per \(\mathrm{kg}\) of air,
respectively, and thus \(0.006 \mathrm{kg}\) of water vapor is condensed and
removed for each kg of air that enters. The refrigerator door is opened an
average of 20 times a day, and each time half of the air volume in the
refrigerator is replaced by the warmer kitchen air. If the refrigerator has a
coefficient of performance of 1.4 and the cost of electricity is 11.5 cents
per \(\mathrm{kWh}\), determine the cost of the energy wasted per year as a
result of opening the refrigerator door. What would your answer be if the
kitchen air were very dry and thus a negligible amount of water vapor
condensed in the refrigerator?
