Problem $2-$

Over the past several decades, artificial refrigerants have begun to be phased out due to their detrimental effects on the ozone layer and global warming. An alternative refrigerant, which has low global warming potential and zero ozone depletion potential, is carbon dioxide $($which is a natural refrigerant$).$ Shown below is a cascade refrigeration cycle which uses ammonia in the hightemperature unit $($Cycle A $)$ and carbon dioxide in the low$-$temperature unit $($Cycle B$).$ The target refrigeration load $(Q_L)$ of the cycle is $1000$ kW $.$ Analyze the provided cycle, given the following information:

$T_3=T_8+5$

$T_7=315K$

$T_4=225K$

a$)$ Setting the outlet temperature of the ammonia $($Cycle A $)$ expansion valve to be $280$ K $($i$.$e$.T_8=280$ K $),$ determine:

The mass flow rates of the two cycles and $($:$m_B^{}$