Question $1(45$ points$)$:

parts. Show calculations and provide logical explanations wherever required.

Shown in the figure below is a compressor, connected to an air$-$cooled heat exchanger. The compressor receives carbon dioxide $(C{O}_2)$ from a source at $100$ kPa and $280$ K with negligible velocity. The $C{O}_2$ leaves the compressor at $1100$ kPa and $500$ K $,$ with a velocity of $25\frac{m}{s}.$ The $C{O}_2$ then flows into a constant$-$pressure heat exchanger, where it is cooled to $350$ K $,$ as it leaves the heat exchanger. The power input to the compressor is $50$ kW$.$ There is no heat loss from the compressor.

Please answer the following:

a$)$ What is the mass flow rate of $C{O}_2($in $k\frac{g}{s})$ through the compressor?

b$)$ What is the rate of heat loss $($in kJ $)$ from $C{O}_2$ as it flows through the he exchanger?

c$)$ If the cooling air enters the heat exchanger at $12C$ at a mass flow rate of $1k\frac{g}{s},$ what is the temperature of air $($in $C)$ as it leaves the heat exchanger? Ignore the kinetic energy effects in the heat exchanger.

Assume $C{O}_2$ and air as ideal gases. Both the compressor and the heat exchanger are in steady state with negligible potential energy effects.