5. If the energy of a system is given as ℰ(?) = ??! where c is...
5. If the energy of a system is given as ℰ(?) = ??! where c is a
constant and x represents
the degree of freedoms, find the average energy per degree of
freedom. Discuss your
answer.
Homework Answers
2. Imagine that the partition function of a system is given by Z), where A is...
2. Imagine that the partition function of a system is given by Z), where A is a 3N A V2 constant. Find average energy, pressure, C, equation of state, compressibility, and thermal expansion coefficient. Find the entropy of this system. Is it free of Gibbs paradox?
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Question#1 : A person wants to install a solar energy system in a given place, where...
Question#1 : A person wants to install a solar energy system in a given place, where at a certain time in the afternoon, the zenith angle is 30degree, the transmittance ofallgases is 70%, the water vapor absorption is 5% and the transmittance of aerosol is 90%. The solar power density a. 100 W/m2 b. 685.5 W/m c. 2050w/m2 d. None of these Question 2:A person wants to install a solar energy system in a given place, where at a certain...
4. (25 pts) The Gibb's free energy of a system of N particles is given by,...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
3(a). Find the equations of motion for the system shown below. The system is two degree...
3(a). Find the equations of motion for the system shown below. The system is two degree of freedom system with degrees of freedom X, and X2. Please find two equations of motion for this dynamical system by both Newtons method and Euler Lagrange. The point with which the spring is attached with the wall has zero displacement indeed) x X2 m2 ki kr Frictionless surfaces on which masses are resting Springs can be assumed to be massless Formulas: Formula to...
31 2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C...
31
2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C decreases its internal energy by 1/5 as a result of condensation at constant pressure. Then, x kJ/kg heat is transferred to the system at constant pressure and 74 kJ/kg work is done with the propeller in the cylinder. (x is taken last two number of each student number) a) Find the degree of quality of the fluid as a result of condensation. (5 POINTS)...
69 2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C...
69
2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C decreases its internal energy by 1/5 as a result of condensation at constant pressure. Then, x kJ/kg heat is transferred to the system at constant pressure and 74 kJ/kg work is done with the propeller in the cylinder. (x is taken last two number of each student number) a) Find the degree of quality of the fluid as a result of condensation. (5 POINTS)...
Suppose that you have a classical equilibrium system that is described by many continuous variables, x1 ..xM with an en...
Suppose that you have a classical equilibrium system that is described by many continuous variables, x1 ..xM with an energy given by: the Ci's and xs are constants. The Ci's are all positive MkBT A) Prove that (E) M regardless of the value of the constants. This result is known as the equipartition theorem each classical quadratic degree of freedom contributes to the average thermal energy of an equilibrium system. kBT B) Use the equipartition theorem to derive the familiar...
Using standard free energy of formation values given in the introduction, calculate the equilibrium constant Kp of the...
Using standard free energy of formation values given in the introduction, calculate the equilibrium constant Kp of the reaction Cl2(g)+2NO(g)⇌2NOCl(g) The standard free energy of the reaction represents the drive the reaction has under standard conditions to move toward equilibrium from point A to point X in the diagram. the equilibrium constant is Kp=1.43x10^7 Calculate the free energy ΔG at 25 ∘C for the nonstandard conditions at point B where the reaction quotient Q is 2.75×10−5. Calculate the free energy...
A gas bottle contains 7.72x1023 Hydrogen molecules at a temperature of 337.0 K. What is the...
A gas bottle contains 7.72x1023 Hydrogen molecules at a temperature of 337.0 K. What is the thermal energy of the gas? (You might need to know Boltzmann's constant: kB = 1.38x10-23 J/K.) Submit Answer How much energy is stored in ONE degree of freedom for the whole system? Submit Answer Tries 0/12 What is the average energy of a single molecule? Submit Answer Tries 0/12 On average how much energy is stored by ONE degree of freedom for ONE single...
2. Imagine that the partition function of a system is given by Z), where A is a 3N A V2 constant. Find average energy, pressure, C, equation of state, compressibility, and thermal expansion coefficient. Find the entropy of this system. Is it free of Gibbs paradox?
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Question#1 : A person wants to install a solar energy system in a given place, where at a certain time in the afternoon, the zenith angle is 30degree, the transmittance ofallgases is 70%, the water vapor absorption is 5% and the transmittance of aerosol is 90%. The solar power density a. 100 W/m2 b. 685.5 W/m c. 2050w/m2 d. None of these Question 2:A person wants to install a solar energy system in a given place, where at a certain...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
3(a). Find the equations of motion for the system shown below. The system is two degree of freedom system with degrees of freedom X, and X2. Please find two equations of motion for this dynamical system by both Newtons method and Euler Lagrange. The point with which the spring is attached with the wall has zero displacement indeed) x X2 m2 ki kr Frictionless surfaces on which masses are resting Springs can be assumed to be massless Formulas: Formula to...
31
2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C decreases its internal energy by 1/5 as a result of condensation at constant pressure. Then, x kJ/kg heat is transferred to the system at constant pressure and 74 kJ/kg work is done with the propeller in the cylinder. (x is taken last two number of each student number) a) Find the degree of quality of the fluid as a result of condensation. (5 POINTS)...
69
2. In a piston cylinder device with 5 kg of saturated vapor at 180 °C decreases its internal energy by 1/5 as a result of condensation at constant pressure. Then, x kJ/kg heat is transferred to the system at constant pressure and 74 kJ/kg work is done with the propeller in the cylinder. (x is taken last two number of each student number) a) Find the degree of quality of the fluid as a result of condensation. (5 POINTS)...
Suppose that you have a classical equilibrium system that is described by many continuous variables, x1 ..xM with an energy given by: the Ci's and xs are constants. The Ci's are all positive MkBT A) Prove that (E) M regardless of the value of the constants. This result is known as the equipartition theorem each classical quadratic degree of freedom contributes to the average thermal energy of an equilibrium system. kBT B) Use the equipartition theorem to derive the familiar...
A gas bottle contains 7.72x1023 Hydrogen molecules at a temperature of 337.0 K. What is the thermal energy of the gas? (You might need to know Boltzmann's constant: kB = 1.38x10-23 J/K.) Submit Answer How much energy is stored in ONE degree of freedom for the whole system? Submit Answer Tries 0/12 What is the average energy of a single molecule? Submit Answer Tries 0/12 On average how much energy is stored by ONE degree of freedom for ONE single...
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