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Problem 4 - Equation of State for a Perfect Gas. Recall the differential form of the...
physical chemistry 3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas...
physical chemistry
3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal g...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Write down the equation that defines entropy in thermodynamics. Define...
A quantity of a certain perfect gas is compressed from an initial state of 0.085 m3,...
A quantity of a certain perfect gas is compressed from an initial state of 0.085 m3, 1 bar to a final state of 0.034 m3, 3.9 bar. The specific heat at constant volume is 0.724 kJ/kg×K, and the specific heat at constant pressure is 1.020 kJ/kg×K. The observed temperature rise is 146K. Calculate the specific gas constant, R, the mass of gas present, and the internal energy of the gas.
PROBLEM C and D Problem 9.6 For a mole of a perfect monoatomic gas, the internal...
PROBLEM C and D
Problem 9.6 For a mole of a perfect monoatomic gas, the internal energy can be expressed as a function of the pressure and volume as a) Write the total differential of U, dU b) Calculate the line integrals J dU for the paths shown below (ci, c2, s): 176 CHAPTER 9. EXACT AND INEXACT DIFFERENTIALS 3 P1 2 P1 P1 3 P1 2 P1 P1 3 P1 2 P1 P1 V1 2V1 2V1 2V1 c) Calculate...
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...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
(17%) Problem 4: A monatomic ideal gas is in a state with volume of Vo at...
(17%) Problem 4: A monatomic ideal gas is in a state with volume of Vo at pressure Po and temperature T . The following questions refer to the work done on the gas, W- -PA 17% Part (a) The gas undergoes an isochoric cooling from its initial state (I-Po-T0). For this process, choose what happens to the energy heat, and work from the following Grade Summary Deductions Potential 100% 0% Submissions OAU > 0, Δυ-o-w. Q < 0, and w...
The Sackur-Tetrode Equation gives the entropy of a sample of n moles of monatomic ideal gas...
The Sackur-Tetrode Equation gives the entropy of a sample of n moles of monatomic ideal gas as a function of its internal energy U and volume V S(U, V) = 5/2 n R + n R In (V/n N_A(4piM U/3nN^2_Ah^2)^3/2) In the equation, R is the gas constant, M is the molar mass, N_4 is Avogadro's number, and h is Plank's constant. The equation can be derived using S = k ln W and directly computing W, the number of...
03:15 points Answer brielly to each of the following questions (a) State the differential form of...
03:15 points Answer brielly to each of the following questions (a) State the differential form of the continuity equation Derive the integral form of the continuity equation from its differential form. Identify all the quantities and indicate the units. () (b) What are the three constitutive relationships to characterize electrical media What is the difference between a linear and a non-linear medium? (2) (c) Starting from the time-harmonic form of Maxwell's equations, derive the wave equation for time- varying magnetic...
Recall the state space representation above. Given the differential equation below, what is the number in...
Recall the state space representation above. Given the
differential equation below, what is the number in B(4,1) (rows,
columns).
5y'''' + 25y''' - 10y'' + 12y' + 100y = u
n x 1 vector ax dt n x n Matrix nx1 vector n x 1 vector dt C) x- Ax +Bu(t) 1x n vectoru(t) n x 1 vector
physical chemistry
3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Write down the equation that defines entropy in thermodynamics. Define...
PROBLEM C and D
Problem 9.6 For a mole of a perfect monoatomic gas, the internal energy can be expressed as a function of the pressure and volume as a) Write the total differential of U, dU b) Calculate the line integrals J dU for the paths shown below (ci, c2, s): 176 CHAPTER 9. EXACT AND INEXACT DIFFERENTIALS 3 P1 2 P1 P1 3 P1 2 P1 P1 3 P1 2 P1 P1 V1 2V1 2V1 2V1 c) Calculate...
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...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
(17%) Problem 4: A monatomic ideal gas is in a state with volume of Vo at pressure Po and temperature T . The following questions refer to the work done on the gas, W- -PA 17% Part (a) The gas undergoes an isochoric cooling from its initial state (I-Po-T0). For this process, choose what happens to the energy heat, and work from the following Grade Summary Deductions Potential 100% 0% Submissions OAU > 0, Δυ-o-w. Q < 0, and w...
The Sackur-Tetrode Equation gives the entropy of a sample of n moles of monatomic ideal gas as a function of its internal energy U and volume V S(U, V) = 5/2 n R + n R In (V/n N_A(4piM U/3nN^2_Ah^2)^3/2) In the equation, R is the gas constant, M is the molar mass, N_4 is Avogadro's number, and h is Plank's constant. The equation can be derived using S = k ln W and directly computing W, the number of...
03:15 points Answer brielly to each of the following questions (a) State the differential form of the continuity equation Derive the integral form of the continuity equation from its differential form. Identify all the quantities and indicate the units. () (b) What are the three constitutive relationships to characterize electrical media What is the difference between a linear and a non-linear medium? (2) (c) Starting from the time-harmonic form of Maxwell's equations, derive the wave equation for time- varying magnetic...
Recall the state space representation above. Given the
differential equation below, what is the number in B(4,1) (rows,
columns).
5y'''' + 25y''' - 10y'' + 12y' + 100y = u
n x 1 vector ax dt n x n Matrix nx1 vector n x 1 vector dt C) x- Ax +Bu(t) 1x n vectoru(t) n x 1 vector
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