The air is compressed to a pressure of 50 bar and then fuel is injected such that 20 Kj of energy is added per mole of air. Determine the compression ratio, the cut off ratio and thermal efficiency of the cycle if Cp of air is 3.5 times the gas constant R.

Mumbai university > Mechanical Engineering > Sem 3 > Thermodynamics

Marks: 12M

Year: May 2016

$p_1=1bar,T_1=300K,p_2=50bar,Q_i=20KJ/mole×35.71=714.2KJ/Kg,$ $C_p=3.5×R=3.5×287=1004.5 J/KgK$ $p_1 v_1=mRT_1$ $100×v_1=0.287×300$ $v_1=0.861m^3$ $p_1 v_1^γ=p_2 v_2^γ$ $1×0.864^1.4=50×v_2^1.4$ $v_2=0.0528m^3$ Compression ratio: r=$\frac{v_1}{v_2} =\frac{0.861}{0.0528}$ r=16.31 $\frac{T_2}{T_1}$ =$r^(γ-1)$=$16.31^(1.4-1)$

=3.055 $T_2$

=300×3.055=916.43K

Heat supplied at constant pressure

$Q_i=C_p (T_3-T_2 )$

714.2=1.0045($T_3$-916.43)

$T_3$=1627.43K

Cut off ratio

ρ=$\frac{T_3}{T_2} =\frac{1627.43}{916.34}$

ρ=1.78

1.78= $\frac{v_3}{v_2}$

1.78= $\frac{v_3}{0.0528}$

$v_3=0.094m^3$

$\frac{T_3}{T_4}$ =$\frac{v_4}{v_3 }^(γ-1)$

$\frac{1627.43}{T_4} =\frac{0.861}{0.094}^(1.4-1)$

$T_4$=671.05K

$η_th$=1-$\frac{(T_4-T_1)}{γ(T_3-T_2 )}$ =1-$\frac{(671.05-300)}{1.4(1627.43-916.43)}$

$η_th$=0.6272

=62.72%