Problem $2-$ Refrigerator Cycle

An ideal vapor$-$compression refrigeration cycle that uses refrigerant $134-$a as its working fluid maintains a condenser at $1000$ kPa and the evaporator at $\backslash (4^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine:

a$)$ the amount of power required to service a $400$ kW cooling load, and

b$)$ the system's COP. Problem $3-$ Otto Cycle $($Octane vs Hydrogen$)$

In a typical Otto cycle, a fuel is combusted with an air mixture to generate a heat input that drives the cycle. In this problem, we'll compare both octane and hydrogen and their environmental effects as fuels.

a$)$ Show a chemically balanced equation where octane fuel $\backslash (\backslash$left$(\backslash$mathrm$\{$C$\}\_\{8\}\backslash$mathrm$\{$H$\}\_\{18\}\backslash$right$)\backslash )$ reacts with pure oxygen $\backslash (\backslash$left$(\backslash$mathrm$\{$O$\}\_\{2\}\backslash$right$)\backslash )$ to create carbon dioxide and other negligible exhaust products. Then calculate how much $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )($in kg $)$ is produced per $1$ kg of octane. Use the molar mass of Octane $\backslash ((114\mathrm{.}23\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\})\backslash )$ and the molar mass of $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}(44\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\})\backslash )$ in this calculation.

b$)$ On a beautiful Sunday afternoon, you decide to go on a joyride to San Francisco. If the total amount of net work your engine exerts during the trip is $13$ Kilowatt hours, how much $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )$ did the trip produce? For this analysis use the Lower Heating Value $($LHV$)$ of octane as $44,427\backslash (\backslash$mathrm$\{$KJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ Assume an ideal otto cycle with a compression ratio $($ r $)$ of $6$ and gamma $(\backslash (\backslash$gamma $\backslash ))$ is known as $1\mathrm{.}4.$

c$)$ Your environmentally conscious friend stops you before you can leave and convinces you to take their brand new hydrogen powered car instead. If their engine still exerts $13$ kilowatt hours of net work with the same compression ratio and the same gamma, how much Hydrogen will be combusted? The molar mass of $\backslash (\backslash$mathrm$\{$H$\}\_\{2\}\backslash )$ is $\backslash (2\mathrm{.}02\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\}\backslash )$ and the Higher Heating Value $($HHV$)$ of $\backslash (\backslash$mathrm$\{$H$\}\_\{2\}\backslash )$ is $\backslash (120\backslash$mathrm$\{$MJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$

d$)$ If we wanted to design an octane powered car that combusts the same quantity of fuel as the hydrogen car, what must the Efficiency of the engine be to achieve that efficiency? Can we design a compression ratio that satisfies this efficiency? If so$,$ calculate the compression ratio.

e$)$ It seems like hydrogen powered cars are pretty good; however, we rarely see these out on the roads. Explain why car manufacturers choose to build gas $($or octane$)$ based engines instead of hydrogen fuel. Problem $3-$ Otto Cycle $($Octane vs Hydrogen$)$

In a typical Otto cycle, a fuel is combusted with an air mixture to generate a heat input that drives the cycle. In this problem, we'll compare both octane and hydrogen and their environmental effects as fuels.

a$)$ Show a chemically balanced equation where octane fuel $\backslash (\backslash$left$(\backslash$mathrm$\{$C$\}\_\{8\}\backslash$mathrm$\{$H$\}\_\{18\}\backslash$right$)\backslash )$ reacts with pure oxygen $\backslash (\backslash$left$(\backslash$mathrm$\{$O$\}\_\{2\}\backslash$right$)\backslash )$ to create carbon dioxide and other negligible exhaust products. Then calculate how much $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )($in kg $)$ is produced per $1$ kg of octane. Use the molar mass of Octane $(\backslash (114\mathrm{.}23\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\}\backslash ))$ and the molar mass of $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}(44\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\})\backslash )$ in this calculation.

b$)$ On a beautiful Sunday afternoon, you decide to go on a joyride to San Francisco. If the total amount of net work your engine exerts during the trip is $13$ Kilowatt hours, how much $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )$ did the trip produce? For this analysis use the Lower Heating Value $($LHV$)$ of octane as $44,427\backslash (\backslash$mathrm$\{$KJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ Assume an ideal otto cycle with a compression ratio $($ r $)$ of $6$ and gamma $(\backslash (\backslash$mathrm$\{\backslash$gamma$\}\backslash ))$ is known as $1\mathrm{.}4.$

c$)$ Your environmentally conscious friend stops you before you can leave and convinces you to take their brand new hydrogen powered car instead. If their engine still exerts $13$ kilowatt hours of net work with the same compression ratio and the same gamma, how much Hydrogen will be combusted? The molar mass of $\backslash (\backslash$mathrm$\{$H$\}\_\{2\}\backslash )$ is $\backslash (2\mathrm{.}02\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$mol$\}\backslash )$ and the Higher Heating Value $($HHV$)$ of $\backslash (\backslash$mathrm$\{$H$\}\_\{2\}\backslash )$ is $\backslash (120\backslash$mathrm$\{$MJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$

d$)$ If we wanted to design an octane powered car that combusts the same quantity of fuel as the hydrogen car, what must the Efficiency of the engine be to achieve that efficiency? Can we design a compression ratio that satisfies this efficiency? If so$,$ calculate the compression ratio.

e$)$ It seems like hydrogen powered cars are pretty good; however, we rarely see these out on the roads. Explain why car manufacturers choose to build gas $($or octane$)$ based engines instead of hydrogen fuel.