[tex]C_p=C_v+R=\frac{5R}{2}+R=\frac{7R}{2}\\ Q_{12}=\nu C_p(T_2-T_1)=\nu\frac{7R}{2}(T_2-T_1)=1*\frac{7*8,31}{2}(500-300)=29,085*200=5817J\\ Q_{23}=\nu RT_2ln\frac{V_3}{V_2}\\p_2=p_1\\p_3=p_4\\T_2=T_3=const.=>p_2V_2=p_3V_3=>\frac{V_3}{V_2}=\frac{p_2}{p_3}=\frac{3*10^5}{10^5}=3\\ Q_{23}=\nu RT_2ln\frac{V_3}{V_2}=1*8,31*500*ln3=4155ln3 \approx4155 J\\ln3\approx lne=1\\Q_{34}=\nu C_p(T_4-T_3)=\nu\frac{7R}{2}(T_4-T_3)=1*\frac{7*8,31}{2}(300-500)=-29,085*200=-5817J\\[/tex]
[tex]T_1=T-4=const=>p_4V_4=p_1V_1=>\frac{V_1}{V_4}=\frac{p_4}{p_1}=\frac{10^5}{3*10^5}=\frac{1}{3} \\ln\frac{1}{3}\approx -1\\ Q_{41}=\nu RT_1ln\frac{V_1}{V_4}=1*8,31*300ln\frac{1}{3} = 2493ln\frac{1}{3} =-2493 J\\Q_p=Q_{12}+Q_{23}=5817+4155=9972 J\\Q_c=Q_{34}+Q_{41}=-5817-2493=-8310 J\\\eta=1-\frac{|Q_c|}{Q_p}=1-\frac{8310}{9972}=1- 0,8334=16,66=>\eta=16,66\%[/tex]
