Respuesta :
Answer:
a)[tex]T_3=4194.64R[/tex]
b) [tex]P_3=916.21lbf/in^2[/tex]
c)[tex]\eta=0.56[/tex]
Explanation:
Given that
Compression ratio(r)=8
We know that [tex]r=\dfrac{V_1}{V_2}[/tex]
[tex]P_=14.2lbf/in^2,T_1=520R[/tex]
mass of air =0.0015 lb
Heat addition=0.9 btu
[tex]T_2=r^{\gamma-1}T_1[/tex]
So
[tex]T_2=8^{1.4-1}\times 520[/tex]
[tex]T_2=1194.64R[/tex]
To find maximum temperature
We know that heat added at constant volume in petrol cycle
[tex]Q=mC_v(T_3-T_2)[/tex]
[tex]0.9 =.0015\times (T_3-T_2)\times 0.21[/tex]
[tex]0.9 =.0015\times (T_3-1194.64)\times 0.21[/tex]
[tex]T_3=4194.64R[/tex]
To find maximum pressure
[tex]P_2=r^{\gamma}P_1[/tex]
[tex]P_2=8^{1.4}\times 14.2[/tex]
[tex]P_2=260.98lbf/in^2[/tex]
[tex]\dfrac{P_3}{P_2}=\dfrac{T_3}{T_2}[/tex]
So [tex]P_3=916.21lbf/in^2[/tex]
To find efficiency
[tex]\eta =1-\dfrac{1}{r^{\gamma-1}}[/tex]
[tex]\eta =1-\dfrac{1}{8^{1.4-1}}[/tex]
[tex]\eta=0.56[/tex]
