Answer:
[tex]a.T_3=1723.8kPa\\b.n=0.563\\c.MEP=674.95kPa[/tex]
Explanation:
a. Internal energy and the relative specific volume at [tex]s_1[/tex] are determined from A-17:[tex]u_1=214.07kJ/kg, \ \alpha_r_1=621.2[/tex].
The relative specific volume at [tex]s_2[/tex] is calculated from the compression ratio:
[tex]\alpha_r_2=\frac{\alpha_r_1}{r}\\=\frac{621.2}{16}\\=38.825[/tex]
#from this, the temperature and enthalpy at state 2,[tex]s_2[/tex] can be determined using interpolations [tex]T_2=862K[/tex] and [tex]h_2=890.9kJ/kg[/tex]. The specific volume at [tex]s_1[/tex] can then be determined as:
[tex]\alpha_1=\frac{RT_1}{P_1}\\\\=\frac{0.287\times 300}{95} m^3/kg\\0.906316m^3/kg[/tex]
Specific volume,[tex]s_2[/tex]:
[tex]\alpha_2=\frac{\alpha_1}{r}\\=\frac{0.906316}{16}m^3/kg\\=0.05664m^3/kg[/tex]
The pressures at [tex]s_2 \ and\ s_3[/tex] is:
[tex]P_2=P_3=\frac{RT_2}{\alpha_2}\\\\=\frac{0.287\times862}{0.05664}\\=4367.06kPa[/tex]
.The thermal efficiency=> maximum temperature at [tex]s_3[/tex] can be obtained from the expansion work at constant pressure during [tex]s_2-s_3[/tex]
[tex]\bigtriangleup \omega_2_-_3=P(\alpha_3-\alpha_2)\\R(T_3-T_2)=P\alpha(r_c-1)\\T_3=T_2+\frac{P\alpha_2}{R}(r_c-1)\\\\=(862+\frac{4367\times 0.05664}{0.287}(2-1))K\\=1723.84K[/tex]
b.Relative SV and enthalpy at [tex]s_3[/tex] are obtained for the given temperature with interpolation with data from A-17 :[tex]a_r_3=4.553 \ and\ h_3=1909.62kJ/kg[/tex]
Relative SV at [tex]s_4[/tex] is
[tex]a_r_4=\frac{r}{r_c}\alpha _r_3[/tex]
=[tex]=\frac{16}{2}\times4.533\\=36.424[/tex]
Thermal efficiency occurs when the heat loss is equal to the internal energy decrease and heat gain equal to enthalpy increase;
[tex]n=1-\frac{q_o}{q_i}\\=1-\frac{u_4-u_1}{h_3-h_2}\\=1-\frac{65903-214.07}{1909.62-890.9}\\=0.563[/tex]
Hence, the thermal efficiency is 0.563
c. The mean relative pressure is calculated from its standard definition:
[tex]MEP=\frac{\omega}{\alpa_1-\alpa_2}\\=\frac{q_i-q_o}{\alpha_1(1-1/r)}\\=\frac{1909.62-890.9-(65903-214.7)}{0.90632(1-1/16)}\\=674.95kPa[/tex]
Hence, the mean effective relative pressure is 674.95kPa
