It is often stated that the refrigerator door should be

QUESTION:

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 \(\mathrm{kg}\) 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?

Equation Transcription:

4°C

20°C

Text Transcription:

4 degree celsius

0.9 m^3

20 degree celsius

95 kPa

0.004 kg

0.006 kg