Question 1: A.) Assume T vs v are the independent variables. The Heimholtz function f can...
Question 1:
A.) Assume T vs v are the independent variables. The Heimholtz
function f can be expressed as a function of T and v. Expand f as
an exact differential.
B.) The Heimholtz function is defined as f = u - Ts. Find the
partial of f with respect to T at constant v.
C.) Draw a T (vertical axis) vs s (horizontal axis) graph. Using
following following formula for the change in entropy for an ideal,
draw the following process.
s2-s1=Cpln(T2/T1)-Rln(P2/P1)
-isentropic process(show the direction in which the pressure
increases)
-Isothermal process(show the direction in which the pressure
increases)
-Isobaric process
Homework Answers
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Question 1:
A.) Assume T vs v are the independent variables. The Heimholtz
function f can...
1.On a pV diagram, draw the path a gas takes as it goes through the following...
1.On a pV diagram, draw the path a gas takes as it goes through the following processes: first it undergoes an isochoric heating process, then that’s followed by an isobaric cooling process, finally it goes back to its original position on the pV diagram by undergoing an isothermal expansion. 2. An ideal gas initially at volume V1, pressure P1, and temperature T1 undergoes an isobaric process that changes its temperature to T2. The gas immediately undergoes an isothermal process that...
An ideal gas undergoes a cycle consisting of the following mechanically reversible steps: An adiabatic compression...
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An Isobaric H2O thermodynamic process: A Mass of 1.5 kg of H2O undergoes a thermodynamic process...
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02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature...
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The partition function at constant V, T is the sum of Boltzmann factors where the sum is over independent states, . Week #10's Lesson showed that Z is related to two state functions, U and F F=-k...
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1. Show that for a classical ideal gas, Q1 alnQ1 NK Hint: Start with the partition function for t...
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Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skippe...
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Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is ...
Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is the maximal domain, D, for the functions f and g? Write D in set notation. (ii) What is the range of f and g? Is either function onto? ii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z00, 2, 04 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding...
In the Circuit below find the phasor Vo of the output voltage vo-y when the input voltage us-f(t) Vs cos(ot) V. Plot 10log {lH(jo)l'3 function using the Bode Diagrams. Assume that all the Resista...
In the Circuit below find the phasor Vo of the output voltage vo-y when the input voltage us-f(t) Vs cos(ot) V. Plot 10log {lH(jo)l'3 function using the Bode Diagrams. Assume that all the Resistance units are in ΚΩ and all the Capacitance units are in μF. 0.25 0.4
In the Circuit below find the phasor Vo of the output voltage vo-y when the input voltage us-f(t) Vs cos(ot) V. Plot 10log {lH(jo)l'3 function using the Bode Diagrams. Assume that all...
An ideal gas undergoes a cycle consisting of the following mechanically reversible steps: An adiabatic compression from Pu V1, T1 to P2, V2, T2 An isobaric expansion from P2, V2, T2 to P3 P2, Vs, T3 - An adiabatic expansion from P3, Vs, Ts to Pa, V4, T4 - A constant-volume process from Pa, V4, T4 to Pi, VV4, T1 (a) Sketch this cycle on a PV diagram (b) Derive an equation that expresses the thermal efficiency (n) of this...
02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. a) Consider entropy S = S(T, V) and derive the equation TdS. Tas = Cvat +T (1) dV. V Show that this equation can be written as follows BT TdS = CydT + PDV where Cv is the thermal capacity at constant volume, B is the isobaric expansiveness and K is isothermal compressibility: b) Consider a gas described by the equation of state...
The partition function at constant V, T is the sum of Boltzmann factors where the sum is over independent states, . Week #10's Lesson showed that Z is related to two state functions, U and F F=-kT lnZ Using these two relations, derive the relationships between Z and the following state functions and C (a) Entropy: S k In Z + kT (oln Z/oT)v (b) Pressure: P- kT (oln ZƠVr (d) Gibbs Free Energy: G-kTInZ + kTV(OlnZ/aV)T (e) Heat Capacity:...
Air in a piston-cylinder undergoes a cycle with the following processes: Process 1-2: Isobaric process from P = 0.1 MPa, T1 = 600K to T2 = 1200K Process 2-3: Isothermal process to state 3 where P3 = 0.05 MPa Process 3-4: Isochoric process to state 4 where P4 = 0.031 MPa Process 4-1: Polytropic process back to state 1 (a) Show the processes in a P-V plot showing the values. Also calculate or state the values of P. V. T...
1. Show that for a classical ideal gas, Q1 alnQ1 NK Hint: Start with the partition function for the classical ideal gas ( Q1) and use above equation to find the value of right-hand side and compare with the value of r we derive in the class. (Recall entropy you derived for classical gas) NK Making use of the fact that the Helmholtz free energy A (N, V, T) of a thermodynamic system is an extensive property of the system....
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
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In the Circuit below find the phasor Vo of the output voltage vo-y when the input voltage us-f(t) Vs cos(ot) V. Plot 10log {lH(jo)l'3 function using the Bode Diagrams. Assume that all the Resistance units are in ΚΩ and all the Capacitance units are in μF. 0.25 0.4
In the Circuit below find the phasor Vo of the output voltage vo-y when the input voltage us-f(t) Vs cos(ot) V. Plot 10log {lH(jo)l'3 function using the Bode Diagrams. Assume that all...
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