1) 1kg H2O; m =1kg; t1 = 0C; t2 = 90C; změna entropie S=?: S = ∫dQ/T; S2 – S1=∫dQ/T; Q=m.c.T; dQ=m.c.dT; S =T1∫T1 m.c.dT/T; S = m.c.lnT2/T1; c = 4180J/kg.K
2) p1=50kPa; p2=100kPa; S1=1m2; S2=1cm2; h=10m; v2=?: S1.v1 = S2.v2→ v1= (S2/S1).v2; ½.ρ.v12 + h1.ρ.g + p1=½.ρ.v22 + h2.ρ.g + p2; ½.ρ.(v12-v12) = p2 - p1 - h1.ρ.g; v2= √2.( p2 - p1 - h1.ρ.g) / (ρ.( (S2/S1) -1)3) d=0,5mm; σ=0,072N/m; m=?: G=F; F=σ.S; m.g=σ.2πr; m =σ.π.d / g
4) r=0,01mm; ρVZ= 1,2kg.m-3; η=24.10-6Pa/s; v=?: Fg-Fo-Fvz=0; m.g – 6.π.η.r.v- (m.ρVZ.g / ρ) =0; V=m/ρ; V.ρ.g – 6. π.η.r.v – 4/3.π.r3.ρVZ.g = 0; v= (4/3. π.r3.g .(ρ- ρVZ)) / 6. π.η.r
5) d1=0,05mm; h=0,2mm; σ=0,072N/m; d2=?: pd=± 2.σ/r; pd= -2.σ/r ---se rozloží : pd1= -2.σ/r1 = -4.σ/d1 a pd2= -2.σ/r2 = -4.σ/d2; Δp=p1- p2 = h.ρ.g; -4.σ/d1 + 4.σ/d2 = h.ρ.g; d2 = 4.σ/ (h.ρ.g +(4.σ/d1))
6) h=20m; p1=50kPa; p2=100kPa; S1=1m2; S2=1mm2; v1=v2=?: S1.v1 = S2.v2→ v1= (S2/S1).v2; ½.ρ.v12 + h1.ρ.g + p1=½.ρ.v22 + h2.ρ.g + p2; ½.ρ.(v12-v12) = p2 - p1 - h1.ρ.g; v2= √2.( p2 - p1 - h1.ρ.g) / (ρ.( (S2/S1) -1)7) d1=3mm;σ=0,072N/m; d2=0,1mm; Δh=?: pd=± 2.σ/r; pd= -2.σ/r ---se rozloží : pd1= -2.σ/r1 = -4.σ/d1 a pd2= -2.σ/r2 = -4.σ/d2; Δp=p1- p2 = h.ρ.g; -4.σ/d1 + 4.σ/d2 = h.ρ.g; h= (4.σ(1/d2 – 1/ d1) )/(ρ.g)
8) Q=150cm3/s; S=0,5cm2; h=?: Q=S.v→ v=Q/S; ½.ρ.v12 + h1.ρ.g + p1=½.ρ.v22 + h2.ρ.g + p2; (p1=p2; v2=0; h1=0); ½.ρ.v12 = h2.ρ.g; h2= ½.v12/g
9) V1 = 5l; p1 = 100kPa; t1 = 20C; V2=1l; p2=?; T2=?; V3=V2;p3=?; t3=t1; : p1.V1κ=p2.V2κ; p2=p1(V1/V2)κ; p1.V1/T1=p2.V2/T2; T2= p2.V2.T1 / p1.V1; p1.V1/T1=p3.V3/T3; p3 = p1.V1.T3 / T1.V3
10) σ=0,072N/m; p=100kPa; h=5cm; r=? kapilary : pd=2.σ/r; pd=h.ρ.g + p; h.ρ.g + p = 2.σ/r; r = 2.σ/ h.ρ.g + p
11) S1=0,03m2; S2=0,02m2; v1= 1m/s; p1=200kPa; p2;v2=? : S1.v1 = S2.v2→ v1= (S1/S2).v1; ½.ρ.v12 + h1.ρ.g + p1=½.ρ.v22 + h2.ρ.g + p2; p2 = ½.ρ.v12 + p1 - ½.ρ.v22
12)Prsten - ρAu=19290kg/m3; ρAg=10490 kg/m3; m=5,12g; mz=4,762g; t=20°C; ρH2O=998,2kg/m3; CAu=?: F=G-Fvz; F=Gz; mz.g=m.g-V.ρ.g; V=m/ρ; (m/ρp).ρ.g =g (m-mz); ρp=(m/(m-mz)).ρ; m=mAu+mAg; V=VAu+VAg; ρAu=mAu/VAu; ρAg=(m-mAu)/VAg; m/ρp=(mAu/VAu)+((m-mAu)/VAg); mAu=((ρ-ρAg). ρAu.m) /((ρAg-ρAu).ρ); CAu=?
13) V1/V2=15; p1 = 98,1kPa; t1 = 50C; p2; t2=?: p1.V1κ=p2.V2κ; p2=p1(V1/V2)κ; p1.V1/T1=p2.V2/T2; T2= p2.V2.T1 / p1.V1
14) V1 = 5l; p1 = 100kPa; V2=1l; p2=?: p1.V1κ=p2.V2κ; p2=p1(V1/V2)κ
1) U0=24V; Ri=3Ω; R,I,Pmax=?: U0=Ri.I+R.I; I=U0/(Ri+R); P=U.I=R.I2; dP/dR=d[U02.R(Ri+R)-2]/dR=U02(Ri+R)-2-2U02.R(Ri+R)-3=0; 1-2R(Ri+R)-1=0; Ri=R; I=U0/(Ri+R); P=R.U02/ R2.
2) U=6V; R1=3Ω; R2=1Ω; R3=4Ω; Qza hod.=?: I=Q/t → Q=I.t; 1/R‘=1/R1+1/R2; R=R‘+R3; I=U/R; Q=I.t; t=[s]
3) I=0,6A; R1=2Ω; R2=4Ω; R3=5Ω; U0=6V; RA=?: U0=RA.I+R.I+R3.I; 1/R‘=1/R1+1/R2; RA= (U0/I) -R‘-R3
4) U=6V; R1=3Ω; R2=2Ω; R3=6Ω; R4=1Ω; I,UV=?: I1=U/(R1+R4); I2=U/(R2+R3); U1=U-R1.I1; U2=U-R2.I2; UV=U1-U2 ???
5) R1=2Ω; R2=1,5Ω; U=6V; I=2A; R3=?: R=U/I; R‘=R-R1; 1/R‘=1/R2+1/R3
???6) U=220V; R1=100Ω; R2=150Ω; t=1h; Qza hod. , U0max., Imax.= ?: R=R1+R2; I=U/R; Q=I/t; t=[s]; U0max.=U Imax.=?
7)U=6V;R1=1Ω; R2=3Ω; UV=2V; R3=?: 1/R‘=1/R1+1/R2; R‘=; I=UV/R3; U=(R‘+R3).I; ; U=(R‘+R3).(UV/R3)→ R3=(UV.R‘)/ (U-UV)
8) U=220V; C=1μF; R=100Ω; f=50Hz; Ief= ?: ZC=1/ω.C=1/(2π.f.C); I=U/Z; Z=√ZR2+ZC2\ ; ZR=100
9) C=100pF; L=10μH; λ=?: f=1/(2π√L.C\); λ=C/f
10) R=100Ω; f=50Hz; L=1H; Uef=220V; Z, Ief= ?: ω=2.π.f; Z2=R2+ω2L2; Ief= Uef/Z
11) L=0,001H; C=1μF; R=3Ω; f, Z=?: f=1/(2π√L.C\); Z2=R2+1/(ω2C2); ω=2.π.f
12) S=5cm2; U=100V; d=1mm; εr=7; Q,C,E=?: ε0=8,85.10-12F/m; C=ε0.εr.(S/d); Q=C.U; E=1/2.C.U2
13) λ=550nm; h=6,626.10-34Js; c=3.108; m,p,E=?: E=h.f=h.c/λ; λ=h/p→p=h/λ; E=m.c2→m=E/c2
14) mz=6.1024kg; κ=6,7.10-11m3/kg.s; úniková rychlost částice- v=?: Fg=κ.m2/r ; Fd=m.v2/r; κ.m2/r = m.v2/r → v=√κ.m/r15) I1=2A; I2=1A; l=1m; a=1m; F=?: μ=4.π.10-7; F=μ.l.I1.I2/2.π.a
16) P=4W; λ=500nm; za t=1s počet fotonů -N,m=?: h=6,626.10-34J.s; E=m.c2=h.f=h.c/λ; m=h/c.λ; N=P.t/E; E= h.c/λ
17) e=1,6.10-17C; ε0=8,85.10-12F/m; me=9,1.10-32kg; r=0,053mm; n,λ,v,Ek=?:F=e2/4.π.ε0.r2; Fd=m.v2/r; m.v2/r=e2/4.π.ε0.r2→v=e√1/π.ε0.r.m.4\; Ek=1/2m.v2 ; 2.π.m.r.v=n.h→n=2. π.m.r.v/h; λ=c/f=h/p=h/m.v; h=6,626.10-34J.s
18) v=500m/s; v1=100m/s; v2=?: v=v1+v2/(1+((v1.v2)/c2)); v2= v -v2 /(1-((v.v2)/c2)).
19) E=2eV; e=1,602.10-19C; f,m,λ=?: h=6,626.10-34J.s;E=h.c/ λ→λ=h.c/E; m=h/c.λ; f=c/λ
20) λ=5.10-7m; c=3.108m; h=6,626.10-34J.s; f,E,Ek,U=?: f=c/λ; E=h.f; U=(h.c)/(e.f); Ek=1/2m.v2
21) U=6V; R1=3Ω; R2=4Ω; R3=5Ω; UV,IC=?: 1/R‘=1/R1+1/R2; R=R‘+R3; I=U/R ; UV=R3.I
22) U=6V; R=12Ω; a=10cm; B=0,5T; M=?: F=I.B.l.sinα=I.B.a; I=U/R; F=U/R.B.a; M=F.a
23) 2 reflexe; α=40; d=0,5μm; f,λ=?: φ=90-α; k.λ/2.d=sinφ→ λ=2d.sinφ/k; f=c/λ