$\backslash ($ P $7\backslash ))$ Solar radiation is incident on the glass cover of a solar collector at a rate of $\backslash (650\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$ The glass transmits $88$ percent of the incident radiation and has an emissivity of $0\mathrm{.}90.$ The hot water needs of a family in summer can be met completely by a collector $1\mathrm{.}5$ m high and $2$ m wide, and tilted $\backslash (40^\{\backslash$circ$\}\backslash )$ from the horizontal. The temperature of the glass cover is measured to be $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ on a calm day when the surrounding air temperature is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The effective sky temperature for radiation exchange between the glass cover and the open sky is $\backslash (-40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Water enters the tubes attached to the absorber plate at a rate of $1\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Assuming the back surface of the absorber plate to be heavily insulated and the only heat loss occurs through the glass cover, determine $($a$)$ the total rate of heat loss from the collector, $($b$)$ the collector efficiency, which is the ratio of the amount of heat transferred to the water to the solar energy incident on the collector, and $($c$)$ the temperature rise of water as it flows through the collector.