Problem $6$: $(35$ pts $)$ Inside of an internal combustion engine, air exists in a chamber capped

by a piston, which is first compressed, then combusts with fuel, and finally ex$-$

pands again, pushing on the piston. We will consider each step of the process,

modeling the air inside as an ideal gas. Assume that the molar composition

of air is $79\%N_2$ and $21\%O_2.$

$($a$)$ After air intake, the full volume of the piston cylinder is occupied by air

at $20C$ and $100$ kPa $.$ What is the molar specific volume $(\frac{m^3}{m}ol)$ of

the air?

$($b$)$ The compression step is an example of an adiabatic process. During this

process for an ideal gas, the quantity $P{V}^{}$ is constant, with $$ for air

being $\frac{7}{5}=1\mathrm{.}4.$ If the air is compressed to $10\%$ of its original volume,

what is the new temperature and pressure?

$($c$)$ The air from $($b$)$ is then mixed with fuel and combusts producing more

gas as a product. Considering the chemical reaction

$2C_8{H}_{18(liq)}+25O_{2(g)}16C{O}_{2(g)}+18H_2{O}_{(g)}$

we can see that for each mol of $O_2$ consumed, $1\mathrm{.}36$ mol of gas are created.

Assume that all $O_2$ is consumed in the reaction. If immediately after

combustion the same volume as in $($b$)$ is occupied by the combustion

products, and these products are at a temperature of $1500C,$ what is

the pressure? Ignore the volume occupied by the liquid fuel.

$($d$)$ Finally, the combustion products from $($c$)$ expand again in an adiabatic

process to return to the original volume. Assume $=1\mathrm{.}4.$ What is the

final temperature and pressure?

Problem $6$: $(35$ pts $)$ Inside of an internal combustion engine, air exists in a chamber capped

by a piston, which is first compressed, then combusts with fuel, and finally ex$-$

pands again, pushing on the piston. We will consider each step of the process,

modeling the air inside as an ideal gas. Assume that the molar composition

of air is $79\%N_2$ and $21\%O_2.$

$($a$)$ After air intake, the full volume of the piston cylinder is occupied by air

at $20C$ and $100$ kPa $.$ What is the molar specific volume $(\frac{m^3}{m}ol)$ of

the air?

$($b$)$ The compression step is an example of an adiabatic process. During this

process for an ideal gas, the quantity $P{V}^{}$ is constant, with $$ for air

being $\frac{7}{5}=1\mathrm{.}4.$ If the air is compressed to $10\%$ of its original volume,

what is the new temperature and pressure?

$($c$)$ The air from $($b$)$ is then mixed with fuel and combusts producing more

gas as a product. Considering the chemical reaction

$2C_8{H}_{18(liq)}+25O_{2(g)}16C{O}_{2(g)}+18H_2{O}_{(g)}$

we can see that for each mol of $O_2$ consumed, $1\mathrm{.}36$ mol of gas are created.

Assume that all $O_2$ is consumed in the reaction. If immediately after

combustion the same volume as in $($b$)$ is occupied by the combustion

products, and these products are at a temperature of $1500C,$ what is

the pressure? Ignore the volume occupied by the liquid fuel.

$($d$)$ Finally, the combustion products from $($c$)$ expand again in an adiabatic

process to return to the original volume. Assume $=1\mathrm{.}4.$ What is the

final temperature and pressure?