Problem $06\mathrm{.}123-$ Cooling food considering content moisture

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 $\backslash (0\mathrm{.}9\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ and average internal temperature is $\backslash (4^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ At any given time, onethird of the refrigerated space is occupied by food items and the remaining $\backslash (0\mathrm{.}6\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ is filled with air. The average temperature and pressure in the kitchen are $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $95$ kPa $,$ respectively. Also, the moisture contents of the air in the kitchen and the refrigerator are $0\mathrm{.}010$ and $0\mathrm{.}004$ kg per kg of air, respectively, and thus $0\mathrm{.}006$ 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 $1\mathrm{.}4$ and the cost of electricity is $\backslash (\backslash$$ $0\mathrm{.}130/\backslash$mathrm$\{$kWh$\}\backslash ),$ 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? Consider the gas constant of air to be $\backslash (\backslash$mathrm$\{$R$\}=0\mathrm{.}287\backslash$mathrm$\{$kPa$\}.\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$K$\}\backslash ),$ the specific heat of air at room temperature to be $\backslash ($ c P$=1\mathrm{.}005\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash$cdot$\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Use data from the tables.

The cost of energy wasted per year as a result of opening the refrigerator door is $\backslash (\backslash$$ $\backslash )$

The cost of energy wasted per year if the kitchen air were very dry is $\backslash (\backslash$$ $\backslash )$