Tłok;p1=0,5Mpa;V1=1m3;p2=0,2Mpa;V2=5m3;L1-2;Q1-2. L1-2=∫_V1^V2pdV=$\frac{\left( p1 + p2 \right)}{2}\left( V2 - V1 \right)\left\lbrack \text{MJ} \right\rbrack \rightarrow Q1 - 2 = U2 - U1 + L1_{2} \rightarrow U = n*\left( \text{Mcv} \right)*T \rightarrow U2 - U1 = \frac{1}{\kappa - 1}\left\lbrack p2v2 - p1v1 \right\rbrack = \lbrack MJ\rbrack \rightarrow Q1_{2} = U2 - U1 + \kappa = \lbrack MJ\rbrack$. Płyn;V1=0.02m3;p=(0.116/V+0.2)*10⁵  Pa; Pm1 = 0, 5MPa; Pm2 = 0MPa; Pot = 0.1MPa; P1 = 0, 6MPa; P2 = 0, 1MPa;L1-2;Lot1-2;Luż1-2;Lt1-2;N=?$\left( \mathbf{no = 320}\frac{\mathbf{1}}{\mathbf{\min}} \right)\mathbf{\rightarrow}p = pm + pt \rightarrow L1 - 2 = \int_{V1}^{V2}{pdv \rightarrow p1 = \left( \frac{0,116}{V1} + 0,2 \right)*10^{5} = 6*10^{5} \rightarrow \frac{0,116}{V1} + 0,2 = 6 \rightarrow \frac{0,116}{V1} = 5,8 \rightarrow V1 = \frac{0,116}{5,8} = \left\lbrack m3 \right\rbrack \rightarrow}p2 = \left( \frac{0,116}{v2} + 0,2 \right)*10^{5} = 1*10^{5} \rightarrow \frac{0,116}{V2} = 0,8 \rightarrow V2 = \frac{0,116}{0,8} = \left\lbrack m3 \right\rbrack \rightarrow L1 - 2 = \int_{p1}^{p2}{p1 = 0,116*10^{5}\ln\frac{p2}{p1} + 0,2*10^{5}\left( P2 - P1 \right) = \left\lbrack J \right\rbrack \rightarrow Lot = Pot\left( V2 - V1 \right) = 10^{5\ }\left( V2 - V1 \right) = \left\lbrack J \right\rbrack \rightarrow L1 - 2 - Lot1 - 2 = \left\lbrack J \right\rbrack \rightarrow Lt1 - 2 = p1*V1 + L1 - 2 - P2V2 = \left\lbrack J \right\rbrack \rightarrow Ni = Lt1 - 2*n0 \rightarrow n0 = \frac{320}{60\ }}\frac{\mathbf{1}}{\mathbf{s}}\mathbf{Objetosc;}Vz = 5m3;pm1 = 0,5MPa;t1 = 20C;Pot = 0,1MPa;tot = 15C;pm2 = 0,12MPa;t2 = 15C;\mathbf{Vr = ? \rightarrow}m2 = \frac{P1*Vz}{RT1} \rightarrow mr = \frac{Pot*Vr}{\text{Tot}} \rightarrow P2Vz + P2Vr = P1Vz*\frac{T2}{T1} + PotVr\frac{T2}{\text{Tot}} \rightarrow \left( p2 - pot\frac{T2}{\text{Tot}} \right)Vr = p1v2*\frac{T2}{T1} - p2*Vz \rightarrow Vr = Vz*\frac{P1*\frac{T2}{T1} - p2}{p2 - pot*\frac{T2}{\text{Tot}}} = \lbrack m3\rbrack$

Ciśnienie;p1=0.1MPa;t1=20c;Δτ1=14;Δτ2=24;m=idem;p2=0.3Mpa;t2=50c;t3=90c;P3=?->$\frac{\mathbf{m}\mathbf{1}\mathbf{R}}{\mathbf{V}}\mathbf{=}\frac{\mathbf{P}\mathbf{1}}{\mathbf{T}\mathbf{1}}\mathbf{\rightarrow}P2 = \frac{P1*T2}{T1} + \left( \frac{\text{mR}}{V} \right)\tau 1*T2 \rightarrow \frac{\text{mR}}{V} \rightarrow \frac{P2 - P1*\frac{T2}{T1}}{\tau 1*T2} \rightarrow P1 = \frac{m1}{V}RT1 \rightarrow P2 = \left( \frac{m1}{V}R + \frac{m}{V}R*\tau 1 \right)T2 \rightarrow P3 \rightarrow P1*\frac{T3}{T1} + \frac{P2 - P1\frac{T2}{T1}}{\tau 1}*\left( \tau 1 + \tau 2 \right)*T3\lbrack Pa\rbrack$;Objetosc(1);V=300l;tO2=27c;pm=6.5bar;pot=0.1MPa;n,m,Vn?;->$p = pm + pot = 6.5*10^{5} + 10^{5}Pa = \left\lbrack \text{MPa} \right\rbrack \rightarrow pV = n\left( \text{MR} \right)T \rightarrow T = t + 273,15 \rightarrow T = 27 + 273,15 = \left\lbrack K \right\rbrack \rightarrow n = \frac{\text{pV}}{\left( \text{MR} \right)T} = \left\lbrack \text{kmol} \right\rbrack \rightarrow m = n*M = \left\lbrack \text{kg} \right\rbrack \rightarrow Vn = V*\frac{P}{\text{pn}}*\frac{\text{Tn}}{T} = \left\lbrack nm3 \right\rbrack;\mathbf{Szyb\ gazowy;}\Delta Vn = 5*10^{5}mm3\ CH4;p1 = 4.52MPa;p2 = 4.38MPa;T = idem;V = idem;\mathbf{Vn2,nm3? \rightarrow}\left\{ p1*V = n1\left( \text{MR} \right)T;p2*V = n2\left( \text{MR} \right)T;n1 - n2 = \Delta n \right\} \rightarrow \left\{ \frac{P1}{P2} = \frac{n1}{n2};n1 - n2 = \Delta n \right\} \rightarrow n2*\frac{P1}{P2} - n2 = \Delta n \rightarrow n2 = \frac{\text{Δn}}{\frac{P1}{P2} - 1} \rightarrow Vn = n\left( \text{MV} \right)n \rightarrow \left( \text{MV} \right)n = \frac{\left( \text{MR} \right)\text{Tn}}{\text{pn}} = \left\lbrack \frac{nm3}{\text{kmol}} \right\rbrack \rightarrow Vn2 = \frac{\text{ΔVn}}{\frac{P1}{P2}\_ 1} = \ldots 10^{6}\left\lbrack nm3 \right\rbrack \rightarrow n = \frac{\text{Vn}}{\left( \text{MV} \right)n} = \ldots 10^{5}\left\lbrack \text{kmol} \right\rbrack \rightarrow m = n*M = \ldots 10^{6}$[kg]

Entalpia:V=5m3,p=pot=0.1MPa,κ=1.4,t1=20C,Q1-2=8*10⁵ J;ΔU;H1-2;t;Δn. pV=mRT->m=$\frac{\text{pV}}{\text{RT}} \rightarrow dm = \frac{- pv}{RT^{2}}dt \rightarrow u = Cv*T \rightarrow dU = d\left( m*u \right) = m*du + u*dm = \frac{\text{PV}}{\text{RT}}*cv*dt + cv*T\left( \frac{- pv}{\text{RT}^{2}} \right)dt = 0 \rightarrow dQ = dU + dH \rightarrow dv = 0 \rightarrow \int_{1}^{2}{dQ = \int_{1}^{2}{dH \rightarrow Q1 - 2 = H1 - 2 = 8*10^{5}J \rightarrow dH = - h*dm = cp*T*\frac{\text{pV}}{10^{5}}*dT = \frac{\kappa}{\kappa - 1}*p*V*dT \rightarrow h = cp*T \rightarrow m = \frac{\text{pv}}{\text{RT}} \rightarrow dm = - \frac{\text{PV}}{\text{RT}^{2}}*dT \rightarrow H1 - 2 = \int_{1}^{2}{dH = \int_{T1}^{T2}{\frac{\kappa}{\kappa - 1}*p*v*\frac{\text{dT}}{T} = \frac{\kappa}{\kappa - 1}*p*v*ln\frac{T2}{T1} = \frac{\kappa}{\kappa - 1}*pV*ln\frac{n1}{n2} \rightarrow n1 = \frac{p1v1}{\left( \text{MR} \right)T1} \rightarrow \Delta n = n1 - n2 \rightarrow H1 - 2 = \Delta n\left( \text{Mcp} \right)T \rightarrow \left( \text{Mcp} \right) = \frac{\kappa}{\kappa - 1}*\left( \text{MR} \right) \rightarrow t = \frac{H1 - 2}{\Delta n*(Mcp)}}}}}$