Homework Answers
All the derivation of is given in the following image:
if you are wondering why I didn't consider differentiating T in both the cases, since T is not a function of V or E, we cannot differentiate it. Same goes for P
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Need complete answer for part B
5) a) Beginning with the fundamental relation, dE = TdS...
5) a) Beginning with the fundamental relation, dE = Tds - PdV, show that S = S(E, D) b) Use the answer to part a to...
5) a) Beginning with the fundamental relation, dE = Tds - PdV, show that S = S(E, D) b) Use the answer to part a to show that: c) Legendre transform S with respect to the conjugate variables (E to obtain the Helmholtz free entropy s and show that the resulting expression for dø indicates that ° = .D Note: The expression dE = Tds - PdV is sufficient proof that E = E(S.V)
5) a) Beginning with the fundamental relation, dE = TDS – PdV, show that S =...
5) a) Beginning with the fundamental relation, dE = TDS – PdV, show that S = S(E,V)
By considering the volume V and entropy S as the two independent variables in the thermodynamic equation dE = TdS−PdV , derive the Maxwell relation between the derivatives ∂T/ ∂V and ∂P/ ∂S .
By considering the volume V and entropy S as the two independent variables in the thermodynamic equation dE = TdS−PdV , derive the Maxwell relation between the derivatives ∂T/ ∂V and ∂P/ ∂S .
A mixture of two monatomic ideal gases consists of Na molecules of gas A and Na...
A mixture of two monatomic ideal gases consists of Na molecules of gas A and Na molecules of gas B in a container of volume V at temperature T. (a) Obtain an expression for natural log of the number of the accessible microstates for each species (ie, ln S, and In Ω), (b) Show that the entropy of the mixture system is 4. EA and Ea are the total energies for the two molecular species, m, and m , the...
These are the chain rules to be used. ЭС ДА Әв -1 дА В Әвс дс...
These are the chain rules to be
used.
ЭС ДА Әв -1 дА В Әвс дс A А 1 A B B 2 Expressions for TdS for Different Independent Variables The differential first law of thermodynamics for a system with a constant number of particles, TdS = dUPdV, can be expressed as a function of either dV and dP, dP and dT or dT and dV. In the lecture, the relation TdS CydT +T& dV has been derived кт a)...
Many times it is useful re-writing partial differential thermodynamic expressions in different forms using the total...
Many times it is useful re-writing partial differential thermodynamic expressions in different forms using the total differentials for E, H, F. and G. The total differentials of E, H, F, and G are: dE = TDS – PdV + udn dH = TDS + VDP + udn dF = -SDT – PdV + udn dG = -SDT + VdP + udn - Part A Rewrite the following expression in terms of S, T, P, V.1, 11, Q, CAm, and/or Cvm,...
Hello physics masters. Need your help wt a partition function multi part question. Please show al...
Hello physics masters. Need your help wt a partition
function multi part question. Please show all
parts, in as much detail as possible for
better learning. Please use your best writing.
Much appreciated. #Thermo #Stat.mechanics
3. The partition function for a system of some kind of particles is reported to be: 3 where (2TmkT)2 and where a and b are constants. (a) Find U(T,V,N). (b) Find p(T,V,N) (c) Find S(U, V,N). (d) Show that your entropy computed above is not...
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...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental Equation for U determine the associated partial derivatives for T and P. Next, determine the associated Maxwell Relation. (b) Starting with the Helmholtz free energy (A = U – TS) derive the associated Fundamental Equation and identify the partial derivative relationships for P and S. Then derive the associated Maxwell Relation.
(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4....
(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4. Let (y,,y2) be fundamental set y'" + a(x)y 0 and let Z y1y2 Show that for the DE (1) Z" + 4a(x)Z' +2a'(x)Z = 0 and zZ" -z)2 +2a(x)Z2 = constant.
(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4. Let (y,,y2) be fundamental set y'" + a(x)y 0 and let Z y1y2 Show that for the...
5) a) Beginning with the fundamental relation, dE = Tds - PdV, show that S = S(E, D) b) Use the answer to part a to show that: c) Legendre transform S with respect to the conjugate variables (E to obtain the Helmholtz free entropy s and show that the resulting expression for dø indicates that ° = .D Note: The expression dE = Tds - PdV is sufficient proof that E = E(S.V)
5) a) Beginning with the fundamental relation, dE = TDS – PdV, show that S = S(E,V)
A mixture of two monatomic ideal gases consists of Na molecules of gas A and Na molecules of gas B in a container of volume V at temperature T. (a) Obtain an expression for natural log of the number of the accessible microstates for each species (ie, ln S, and In Ω), (b) Show that the entropy of the mixture system is 4. EA and Ea are the total energies for the two molecular species, m, and m , the...
These are the chain rules to be
used.
ЭС ДА Әв -1 дА В Әвс дс A А 1 A B B 2 Expressions for TdS for Different Independent Variables The differential first law of thermodynamics for a system with a constant number of particles, TdS = dUPdV, can be expressed as a function of either dV and dP, dP and dT or dT and dV. In the lecture, the relation TdS CydT +T& dV has been derived кт a)...
Many times it is useful re-writing partial differential thermodynamic expressions in different forms using the total differentials for E, H, F. and G. The total differentials of E, H, F, and G are: dE = TDS – PdV + udn dH = TDS + VDP + udn dF = -SDT – PdV + udn dG = -SDT + VdP + udn - Part A Rewrite the following expression in terms of S, T, P, V.1, 11, Q, CAm, and/or Cvm,...
Hello physics masters. Need your help wt a partition
function multi part question. Please show all
parts, in as much detail as possible for
better learning. Please use your best writing.
Much appreciated. #Thermo #Stat.mechanics
3. The partition function for a system of some kind of particles is reported to be: 3 where (2TmkT)2 and where a and b are constants. (a) Find U(T,V,N). (b) Find p(T,V,N) (c) Find S(U, V,N). (d) Show that your entropy computed above is not...
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...
5. (25 points For credit; show every step in the derivations. (a) Starting with the Fundamental Equation for U determine the associated partial derivatives for T and P. Next, determine the associated Maxwell Relation. (b) Starting with the Helmholtz free energy (A = U – TS) derive the associated Fundamental Equation and identify the partial derivative relationships for P and S. Then derive the associated Maxwell Relation.
(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4. Let (y,,y2) be fundamental set y'" + a(x)y 0 and let Z y1y2 Show that for the DE (1) Z" + 4a(x)Z' +2a'(x)Z = 0 and zZ" -z)2 +2a(x)Z2 = constant.
(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4. Let (y,,y2) be fundamental set y'" + a(x)y 0 and let Z y1y2 Show that for the...
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