$(100$ Points$)$ Fully analyze the ideal cycle, considering constant heat capacities for ideal air at room temperature of $27C.$ The piston$-$cylinder assembly forms a closed system. Assume air$-$standard, steadystate conditions, and neglect kinetic energy and potential energy changes, so that $\frac{?}{{?}_{\frac{?}{?}}KE}\frac{?}{{?}_{\frac{?}{?}}}=PE=0.$ The corres

The compresion process ends at state $2,$ while the addition of heat ends at $T_3$ and $P_s.$ Use the given air $($working fluid$)$ data

$R=0\mathrm{.}287k\frac{P_{t,m^3}}{K}g.K=0\mathrm{.}257\frac{k}{K}\frac{g}{K},k=1\mathrm{.}4.,r_c=\frac{V_1}{V_2}=8$

$c_p=1\mathrm{.}005k\frac{.}{\frac{?}{?}}Kg.K,r_t=0\mathrm{.}71sk.\frac{J}{K}g.K$

$T_1=300K=27C.,P_1=100$kPa

$q_n=q_{23}=820k\frac{J}{K}g$

Temperature: $0C=273K$

$2\mathrm{.}1$ For an ideal air, specific volume at state$-1$ is

a$.v_1=0\mathrm{.}86100\frac{m^3}{K}g$

b$.v_1=0\mathrm{.}06105\frac{m^3}{K}g$

c$.v_1=0\mathrm{.}52362\frac{m^3}{K}g$

d$.$ None of the above

$2\mathrm{.}2$ From the compression ratio, the state$-2$ specific volume is

a$.v_2=0\mathrm{.}05423\frac{m^3}{K}g$

b$.v_2=0\mathrm{.}10763\frac{m^3}{K}g$

c$.v_2=0\mathrm{.}18451\frac{m^3}{K}g$

d$.$ None of the above

$2\mathrm{.}3$ The state$-2$ temperature is

a$.T_2=578\mathrm{.}12C$

b$.T_2=478\mathrm{.}23C$

c$.T_2=416\mathrm{.}22C$

d$.$ None of the above

$2\mathrm{.}4$ For an ideal air, the state$-2$ pressure is

a$.P_2=1837\mathrm{.}83$kPa

b$.P_2=2145\mathrm{.}23$kPa

c$.P_2=3005\mathrm{.}86$kPa

d$.$ None of the above

$2\mathrm{.}5$ For the ideal process $1-2,$ the pressure becomes

a$.P_2=1837\mathrm{.}92$kPa

b$.P_2=2145\mathrm{.}23$kPa

c$.P_2=3005\mathrm{.}86$kPa

d$.$ None of the above

$2\mathrm{.}6$ The state$-2$ average pressure value is

a$.P_2=1924\mathrm{.}12$kPa

b$.P_2=1837\mathrm{.}88$kPa

c$.P_2=1723\mathrm{.}58$kPa

d$.$ None of the above

$2\mathrm{.}7$ The state$-3$ temperature is

a$.T_3=1623\mathrm{.}08C$

b$.T_3=1456\mathrm{.}13C$

c$.T_3=1558\mathrm{.}28C$

d$.$ None of the above

$2\mathrm{.}8$ For the isochoric process $2-3$ with $v_2=v_3=0\mathrm{.}10763\frac{m^3}{K}g,$ the state$-3$ pressure is

a$.P_3=4883\mathrm{.}31$kPa

b$.P_3=2547\mathrm{.}13$kPa

c$.P_3=3587\mathrm{.}21$kPa

d$.$ None of the above

$2\mathrm{.}9$ For isentropic process $3-4$ and ideal gas with $v_4=v_1=0\mathrm{.}86100\frac{m^3}{K}g$$$,$ the state$-4$ temperature is

a$.T_4=609\mathrm{.}23C$

b$.T_4=524\mathrm{.}11C$

c$.T_4=711\mathrm{.}258C$

d$.$ None of the above

$2\mathrm{.}10$ For an ideal gas, the state$-4$ pressure is

a$.P_4=301\mathrm{.}211$kPa

b$.P_4=451\mathrm{.}34$kPa

c$.P_4=265\mathrm{.}70$kPa

d$.$ None of the above

$2\mathrm{.}11$ The specific internal energy values are $u_1=215\mathrm{.}40k\frac{J}{K}g,u_2=494\mathrm{.}86k\frac{J}{K}g,u_3=1314\mathrm{.}86k\frac{J}{K}g$ and $u_4=572\mathrm{.}32k\frac{J}{K}g$

a$.$ True

b$.$ False

$2\mathrm{.}12$ The change in specific internal energy values are $u_{12}=279\mathrm{.}06k\frac{J}{K}g,u_{23}=820\mathrm{.}00k\frac{J}{K}g,u_{34}=-742\mathrm{.}54k\frac{J}{K}g$ and $u_{41}=-356\mathrm{.}92k\frac{J}{K}g$

a$.$ True

b$.$ False

$2\mathrm{.}13$ For process $1-2,$ the specific work done is

a$.w_{12}=-279\mathrm{.}06k\frac{J}{K}g$

b$.w_{12}=-451\mathrm{.}34k\frac{J}{K}g$

c$.w_{12}=265\mathrm{.}70k\frac{J}{K}g$

d$.$ None of the above

$2\mathrm{.}14$ For process $2-3,$ the heat transfer is

a$.q_{23}=755\mathrm{.}216k\frac{J}{K}g$

b$.q_{23}=820\mathrm{.}00k\frac{J}{K}g$

c$.q_{23}=-688\mathrm{.}54k\frac{J}{K}g$

d$.$ None of the above

$2\mathrm{.}15$ For process $3-4,$ the specific work done is

a$.w_{34}=-677\mathrm{.}33k\frac{J}{K}g$

c$.w_{34}=742\mathrm{.}54k\frac{J}{K}g$

b$.w_{34}=821\mathrm{.}65k\frac{J}{K}g$

d$.$ None of the above

$2\mathrm{.}16$ For process $4-1,$ the heat transfer is

a$.q_{41}=-356\mathrm{.}92k\frac{J}{K}g$

b$.q_{41}=850\mathrm{.}08k\frac{J}{K}g$

c$.q_{41}=-209\mathrm{.}54k\frac{J}{K}g$

d$.$ None of the above

$2\mathrm{.}17$ The ideal net work out due to the heat transfer processes becomes

a$.w_{\text{n}\text{e}\text{t},q}=463\mathrm{.}08k\frac{J}{K}g$

b$.w_{\text{n}\text{e}\text{t},q}=224\mathrm{.}58k\frac{J}{K}g$

<

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