Problem $2$: Consider a refrigerator whose dimensions are $\backslash (1\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash$times $1\mathrm{.}2\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )$ and whose walls are $3$ cm thick. The refrigerator consumes $600$ W of power when operating and has a COP of $2\mathrm{.}5.$ It is observed that the motor of the refrigerator remains on for $5$ minutes and then is off for $15$ minutes periodically. If the average temperatures at the inner and outer surfaces of the refrigerator are $\backslash (6^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (17^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ respectively, determine the average thermal conductivity of the refrigerator walls. Also, determine the annual cost of operating this refrigerator if the unit cost of electricity is $\backslash (\backslash$$ $0\mathrm{.}08/\backslash$mathrm$\{$kWh$\}\backslash ).$