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Choose one equation (and only one) from the equation sheet that would let you solve the problem posed. Then define which variables in the equation go with what numbers from the problem itself (not from other problems), and define which variable is being solved for. Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown. Don’t forget to include direction when called for by a vector variable. 1) A single mole of Carbon Dioxide has a mass of 44 g, and at 1.00 atm of pressure and 20oC (293K) it occupies 22.4 liters. At what speed will you find the peak of its speed distribution function?

Choose one equation (and only one) from the equation sheet that would let you solve the problem posed. Then define which variables in the equation go with what numbers from the problem itself (not from other problems), and define which variable is being solved for. Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown. Don’t forget to include direction when called for by a vector variable. 1) A single mole of Carbon Dioxide has a mass of 44 g, and at 1.00 atm of pressure and 20oC (293K) it occupies 22.4 liters. At what speed will you find the peak of its speed distribution function?

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Choose one equation (and only one) from the equation sheet that would let you solve the problem posed. Then define which variables in the equation go with what numbers from the problem itself (not from other problems), and define which variable is being solved for. Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown. Don’t forget to include direction when called for by a vector variable. 1) A single mole of Carbon Dioxide has a mass of 44 g, and at 1.00 atm of pressure and 20oC (293K) it occupies 22.4 liters. At what speed will you find the peak of its speed distribution function?
x(t) = x0 + Voxt + ½ axt² y(t) = yo + Voyt + ½ ayt² Vx (t) = Vox? + 2ax(x-xo) Vy (t) = Voy + 2a,(y-yo) v(t) = dx/dt a(t) = d?x/dt? Vx(t) = Vox + axt Vy(t) = Voy + ayt <V> = (vo + V1) / 2 <a> = (V1 – Vo)/(tj – to) r = x² + y? (Vo + V1) / 2 = Ar/At a(t) = dv/dt x = rcose <V> = Ar/At <a> = Av/At |A| = (A,? + A,?)2 Â = A y = rsin0 a = ac(-f) + arê® ac = Vr/r a. = m²r VT = (2nr)/T ac = 4n°r/T? ar = dvf/dt VT = or f = o/2n f = 1/T rP/A = rP/B + rB/A VP/A = VP/B + VB/A ap/A = ap/B + aB/A m, m2 EF¡ = ma F12 = -F21 = G (-12) fs,max = lsFN F = mv²/r fk = µkFN Fe = mac Fdrag = -by Fdrag = ½ DpAv² (-8) 2mg Vt = mg/b Vt = dW; = F; · dr Wi = F; · Ar Ug = mgy AUint = fgAs n = Pout/Pin (X 100%) V DpA K = ½ mv? Usp = ½ k(x-xrel)? P = dW/dt AK = ½ m (v1²-vo²) Fsp = -k (x-Xrel) P = dU/dt = dp/dt ΣW ΔΚ P = F•v <ΣF-Δp/Δt p= mv miv10 + m2v20 = m¡v11 + m2V21 ½ miV10? + ½ m2V20? = ½ m¡V11? + ½ m2v21? m¡V10 + m2v20 = (m¡+m2)VTI (mi+m2)VT0 = m¡Vj1 + m2V21 (m2-m1 m,+m2 (Em;) Zem = E(m;z;) (mi-m2) V10 + m1+m2/ 2m2 2m1 V11 V20 V21 = V20 + |V10 \m,+m2/ (Σm) xem- Σ(mx ) Av, = +Ve In(M/M¡) 0 = 0o + @ot + ½ at² \m,+m2/ (Σm ) yem Σ(my ) Fth = v(dm/dt) mtotalXCM = o? = 00? + 2a(0–0) @ = Wo + at <a> = A@/At <@> = AÐ/At Vcm = ro S = r0 a(t) = d²0/dt? T = rleverF TAB = -TBA I= Iem + Md² @(t) = d0/dt a(t) = d@/dt T = rFsino Et = dL/dt I = BMR? L =r xp T =r x F dW; = t;· de I= E m,r;? Op = (mgrsin0)/(Io) Στ-Ια Krot = ½ Io? rjever = rsino I010 + I2020 = I011 + I2021 (I1+I2)@ro = I10i1 + I2@21 L = Io ΔL TΔt I010 + I2020 = (I1+I2)@T1 I10010 = I1101 1/2
Transcribed Image Text:x(t) = x0 + Voxt + ½ axt² y(t) = yo + Voyt + ½ ayt² Vx (t) = Vox? + 2ax(x-xo) Vy (t) = Voy + 2a,(y-yo) v(t) = dx/dt a(t) = d?x/dt? Vx(t) = Vox + axt Vy(t) = Voy + ayt <V> = (vo + V1) / 2 <a> = (V1 – Vo)/(tj – to) r = x² + y? (Vo + V1) / 2 = Ar/At a(t) = dv/dt x = rcose <V> = Ar/At <a> = Av/At |A| = (A,? + A,?)2 Â = A y = rsin0 a = ac(-f) + arê® ac = Vr/r a. = m²r VT = (2nr)/T ac = 4n°r/T? ar = dvf/dt VT = or f = o/2n f = 1/T rP/A = rP/B + rB/A VP/A = VP/B + VB/A ap/A = ap/B + aB/A m, m2 EF¡ = ma F12 = -F21 = G (-12) fs,max = lsFN F = mv²/r fk = µkFN Fe = mac Fdrag = -by Fdrag = ½ DpAv² (-8) 2mg Vt = mg/b Vt = dW; = F; · dr Wi = F; · Ar Ug = mgy AUint = fgAs n = Pout/Pin (X 100%) V DpA K = ½ mv? Usp = ½ k(x-xrel)? P = dW/dt AK = ½ m (v1²-vo²) Fsp = -k (x-Xrel) P = dU/dt = dp/dt ΣW ΔΚ P = F•v <ΣF-Δp/Δt p= mv miv10 + m2v20 = m¡v11 + m2V21 ½ miV10? + ½ m2V20? = ½ m¡V11? + ½ m2v21? m¡V10 + m2v20 = (m¡+m2)VTI (mi+m2)VT0 = m¡Vj1 + m2V21 (m2-m1 m,+m2 (Em;) Zem = E(m;z;) (mi-m2) V10 + m1+m2/ 2m2 2m1 V11 V20 V21 = V20 + |V10 \m,+m2/ (Σm) xem- Σ(mx ) Av, = +Ve In(M/M¡) 0 = 0o + @ot + ½ at² \m,+m2/ (Σm ) yem Σ(my ) Fth = v(dm/dt) mtotalXCM = o? = 00? + 2a(0–0) @ = Wo + at <a> = A@/At <@> = AÐ/At Vcm = ro S = r0 a(t) = d²0/dt? T = rleverF TAB = -TBA I= Iem + Md² @(t) = d0/dt a(t) = d@/dt T = rFsino Et = dL/dt I = BMR? L =r xp T =r x F dW; = t;· de I= E m,r;? Op = (mgrsin0)/(Io) Στ-Ια Krot = ½ Io? rjever = rsino I010 + I2020 = I011 + I2021 (I1+I2)@ro = I10i1 + I2@21 L = Io ΔL TΔt I010 + I2020 = (I1+I2)@T1 I10010 = I1101 1/2
F ΔF ΔΡ Y = B = B = AV S = Vo x(t) = Xmax cOs(@t + 0) T= 27 (L/g)'2 @ = (k/m)'2 T= 27 (I/mgd)"2 Vmax = OXmax amax = 0ʻxmax y(x,t) = ymax Ssin(kx + @t + þ) v = f. a?y Odamped = ( (k/m) – (b/2m)² )'/² y(x,t) = ymax sin(kx - ot + ¢) 2 = 2n/k v = @/k 1 д?у v = (Fr/u)2 µ = m/L <Pwave> = ½ uymax-@ʻv əx² v² at2 ΔΡ %3D max Bksmax AP, = pwvsSmax Vsound = Vsound = 343 m/s max TC Vsound = (331-) 1+ Vsound 331 m/s + (0.60 m/s°C) Tc 273 °C APmax I = 2ρν 10 dB = 1 B <P> B = log () P = pvosmax A sin°(kx-@t) I, = 10-12 W/m² (exactly) I = %3D 4tr2 fobserver = fsource (Vsound+Vobserver sin(A) + sin(B) = 2 cos (-4): sin () Vsound-Vsource 0 = 2tn (const) 0 = T(2n+1) (dest) An = 4L/(2n-1) fn = (2n-1)v/4L AV = V.B(T1-To) AL=La(T1-To) Q = mLv AEint = W + Q n = 0, ±1, ±2,.. An = 2L/n fn = nv/2L n = 1, 2, 3, ... Af = |f1 – f2| B= 3a Q = mLf AEcyele PV = nRT Q = mcAT W = - SP dV AT = Tinal - Tinitial Wisobaric = -PAV Vfinal \Vinitial- = 0 Wisovolumetric = 0 Qadiabatic = 0 Qisothermal = nRT In R = Ax/k 4 Pradiated = GAETK* TK = Tc + 273.15 Ktot = ( ½ NKBT) * degrees of freedom (dof) 8kgT P = kA|dT/dx| Pnet = GAe (Tsource – Tobject") ½ mo<v?> = ½ kgT 3kgT kB = R/NA 2kgT VRMS = Vavg Vmost likely mo Timo V mo 3RT 8RT 2RT VRMS = Vavg Vmost likely M M AEint = Q = nCyAT Q=nCpAT P¡V = P2V2Y CoP = |Q/|W| dS = dQreversible/T ASfree expand = nR In(V2/V1) Ср 3D Су + R Y = Cp/Cy n = |W]/lQH| Cy = ½ R * dof T¡V;! = T2V;*1 n = 1 – (IQc/IQH|) Notto = 1– (V2/V)-! = 0 NCarnot = 1 – (T/TH) ASCarnot %3D
Transcribed Image Text:F ΔF ΔΡ Y = B = B = AV S = Vo x(t) = Xmax cOs(@t + 0) T= 27 (L/g)'2 @ = (k/m)'2 T= 27 (I/mgd)"2 Vmax = OXmax amax = 0ʻxmax y(x,t) = ymax Ssin(kx + @t + þ) v = f. a?y Odamped = ( (k/m) – (b/2m)² )'/² y(x,t) = ymax sin(kx - ot + ¢) 2 = 2n/k v = @/k 1 д?у v = (Fr/u)2 µ = m/L <Pwave> = ½ uymax-@ʻv əx² v² at2 ΔΡ %3D max Bksmax AP, = pwvsSmax Vsound = Vsound = 343 m/s max TC Vsound = (331-) 1+ Vsound 331 m/s + (0.60 m/s°C) Tc 273 °C APmax I = 2ρν 10 dB = 1 B <P> B = log () P = pvosmax A sin°(kx-@t) I, = 10-12 W/m² (exactly) I = %3D 4tr2 fobserver = fsource (Vsound+Vobserver sin(A) + sin(B) = 2 cos (-4): sin () Vsound-Vsource 0 = 2tn (const) 0 = T(2n+1) (dest) An = 4L/(2n-1) fn = (2n-1)v/4L AV = V.B(T1-To) AL=La(T1-To) Q = mLv AEint = W + Q n = 0, ±1, ±2,.. An = 2L/n fn = nv/2L n = 1, 2, 3, ... Af = |f1 – f2| B= 3a Q = mLf AEcyele PV = nRT Q = mcAT W = - SP dV AT = Tinal - Tinitial Wisobaric = -PAV Vfinal \Vinitial- = 0 Wisovolumetric = 0 Qadiabatic = 0 Qisothermal = nRT In R = Ax/k 4 Pradiated = GAETK* TK = Tc + 273.15 Ktot = ( ½ NKBT) * degrees of freedom (dof) 8kgT P = kA|dT/dx| Pnet = GAe (Tsource – Tobject") ½ mo<v?> = ½ kgT 3kgT kB = R/NA 2kgT VRMS = Vavg Vmost likely mo Timo V mo 3RT 8RT 2RT VRMS = Vavg Vmost likely M M AEint = Q = nCyAT Q=nCpAT P¡V = P2V2Y CoP = |Q/|W| dS = dQreversible/T ASfree expand = nR In(V2/V1) Ср 3D Су + R Y = Cp/Cy n = |W]/lQH| Cy = ½ R * dof T¡V;! = T2V;*1 n = 1 – (IQc/IQH|) Notto = 1– (V2/V)-! = 0 NCarnot = 1 – (T/TH) ASCarnot %3D
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