Mathematically prove that the maximum entropy of mixing of two gases A and B is achieved...
Mathematically prove that the maximum entropy of mixing of two gases A and B is achieved at Xa:Xb = 1:1 molar fraction ratio.
Homework Answers
Delta Gmix= - Delta Smix / T
Where G mix = Gibb's free energy of mixing
S mix = Entropy of mixing
Entropy of mixing is maximum when Gibb's free energy of mixing is minimum or decrease is maximum.
So with this concept in mind I have shown the calculation for Gibb's free energy of mixing.
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Mathematically prove that the maximum entropy of mixing of two
gases A and B is achieved...
(a) Show that the entropy of mixing for two volumes of monatomic ideal gases A and...
(a) Show that the entropy of mixing for two volumes of monatomic
ideal gases A and B starting from equal temperatures and pressures
is given by:
where N is the total number of atoms and fA and fB are the
fraction of atoms that are type A and B, respectively, so that fA +
fB = 1.
ASmiring = -kNISA In(fa)+fe In(fB) = -kN[fa In(fa)+fi-f, In(fi-f)
2. Determine the change in entropy for an isothermal process in which two initially separated gas...
Please answer ALL parts and show
work/explain
2. Determine the change in entropy for an isothermal process in which two initially separated gases come 1 mol both together where the final volume is just the sum of the two gases's initial volumes. Determine AS for this gases process for 1 mol of gas A at 2 atm and 1 mol of gas B at 1 atm. It is easiest to do this problem in steps. a) Determine the entropy for...
The maximum entropy distribution is Gaussian with two constraints. Use the Lagrange multiplier method to prove...
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Mixing! n moles of Ar and In moles of Xe (treated as ideal gases) are in...
Mixing! n moles of Ar and In moles of Xe (treated as ideal gases) are in adjacent containers with volumes of V and 2V, respectively. The barrier between the two gases is removed, and the two gases mix. Heat and work are not exchanged with the surroundings. Since the two gases start at the same temperature and pressure, the temperature and pressure must not change during mixing. What are delta U, delta H, and delta S for the system after...
Air is a mixture of gases with the following mass percentage composition: 75.52% N2, 23.15% O2,...
Air is a mixture of gases with the following mass percentage
composition: 75.52% N2, 23.15% O2, 1.28% Ar, and 0.046% CO2 (a)
What are the partial pressures of N2, O2, Ar, and CO2, when the
total pressure is 1.100 atm? (b) Calculate the molar Gibbs energy
of mixing of air at 25 °C assuming ideal-gas behavior. (c)
Determine the molar enthalpy of mixing and the molar entropy of
mixing for air at 1.100 atm and 25 °C.
5. (3 pts)...
What is the entropy change for mixing 1 liter of a monoatomic ideal gas (call it...
What is the entropy change for mixing 1 liter of a monoatomic ideal gas (call it A) at 2 atm at 100 oC with 2 liters of a different monoatomic ideal gas (call it B) at 0.5 atm at 0 oC (the total volume is confined to 3 liters)? Assume CV= 1.5R for both gases. (Hint: you need to include the entropy change for the change in volume, change in temperature, and for mixing)
3. For diatomic ideal gases at room temperature, find out the change in entropy due to mixing using the following parti...
3. For diatomic ideal gases at room temperature, find out the change in entropy due to mixing using the following partition functions hv expl2kT T V( h2 Ztranslation rotation vibration h2 hv 1 exp 4. For solids, Einstein the vibrational levels given energy are as hv, j-0,1,2,.. Assuming that the N 2 strongly coupled atoms are +=3 equivalent to 3N simple harmonic independent oscillators, find out the followings (a) Equation for the vibrational energy as a function of temperature (b)...
4. The graph on the right shows the chemical potential of two pure gases, A and...
4. The graph on the right shows the chemical potential of two pure gases, A and B, as a function of temperature at the standard pressure of 1 bar. (a) Circle the correct statement bu A(T) (1) The standard molar entropies of A and B are equal to each other at temperature T u B(T) (ii) The standard molar entropy of substance A is greater than the molar entropy of substance B at temperatures below T, (iii) The standard molar...
Asking for Q3,4,5,6. Mixing Gases Consider two containers, . Both have volume 0.1 m3, and pressure...
Asking for Q3,4,5,6.
Mixing Gases Consider two containers, . Both have volume 0.1 m3, and pressure 106 pa One contains monatomic (3 degrees of freedom) He at T 128 K and One contains diatomic (5 degrees of freedom) N2 at T- 258 K. A valve is opened allowing these two gases to mix. They are kept thermally isolated from the outside You can treat them as i deal gases. 1) What is the change in internal energy under this process?...
Two rigid tanks are connected by a valve. Initially, one tank contains 10 mº of helium...
Two rigid tanks are connected by a valve. Initially, one tank contains 10 mº of helium (He) gas at 220 kPa, 40°C? The other tank initially contains 4.0 R of neon (Ne) gas at 150 kPa, sot. Now the valve is opened, allowing the two gases to mix with each other. Heat transfer occurs during the mixing process. The final equilibrium temperature is 44'C. The specific heats of monatomic gases are independent of temperature. Determine: (a) the final volume of...
(a) Show that the entropy of mixing for two volumes of monatomic
ideal gases A and B starting from equal temperatures and pressures
is given by:
where N is the total number of atoms and fA and fB are the
fraction of atoms that are type A and B, respectively, so that fA +
fB = 1.
ASmiring = -kNISA In(fa)+fe In(fB) = -kN[fa In(fa)+fi-f, In(fi-f)
Please answer ALL parts and show
work/explain
2. Determine the change in entropy for an isothermal process in which two initially separated gases come 1 mol both together where the final volume is just the sum of the two gases's initial volumes. Determine AS for this gases process for 1 mol of gas A at 2 atm and 1 mol of gas B at 1 atm. It is easiest to do this problem in steps. a) Determine the entropy for...
Mixing! n moles of Ar and In moles of Xe (treated as ideal gases) are in adjacent containers with volumes of V and 2V, respectively. The barrier between the two gases is removed, and the two gases mix. Heat and work are not exchanged with the surroundings. Since the two gases start at the same temperature and pressure, the temperature and pressure must not change during mixing. What are delta U, delta H, and delta S for the system after...
Air is a mixture of gases with the following mass percentage
composition: 75.52% N2, 23.15% O2, 1.28% Ar, and 0.046% CO2 (a)
What are the partial pressures of N2, O2, Ar, and CO2, when the
total pressure is 1.100 atm? (b) Calculate the molar Gibbs energy
of mixing of air at 25 °C assuming ideal-gas behavior. (c)
Determine the molar enthalpy of mixing and the molar entropy of
mixing for air at 1.100 atm and 25 °C.
5. (3 pts)...
3. For diatomic ideal gases at room temperature, find out the change in entropy due to mixing using the following partition functions hv expl2kT T V( h2 Ztranslation rotation vibration h2 hv 1 exp 4. For solids, Einstein the vibrational levels given energy are as hv, j-0,1,2,.. Assuming that the N 2 strongly coupled atoms are +=3 equivalent to 3N simple harmonic independent oscillators, find out the followings (a) Equation for the vibrational energy as a function of temperature (b)...
4. The graph on the right shows the chemical potential of two pure gases, A and B, as a function of temperature at the standard pressure of 1 bar. (a) Circle the correct statement bu A(T) (1) The standard molar entropies of A and B are equal to each other at temperature T u B(T) (ii) The standard molar entropy of substance A is greater than the molar entropy of substance B at temperatures below T, (iii) The standard molar...
Asking for Q3,4,5,6.
Mixing Gases Consider two containers, . Both have volume 0.1 m3, and pressure 106 pa One contains monatomic (3 degrees of freedom) He at T 128 K and One contains diatomic (5 degrees of freedom) N2 at T- 258 K. A valve is opened allowing these two gases to mix. They are kept thermally isolated from the outside You can treat them as i deal gases. 1) What is the change in internal energy under this process?...
Two rigid tanks are connected by a valve. Initially, one tank contains 10 mº of helium (He) gas at 220 kPa, 40°C? The other tank initially contains 4.0 R of neon (Ne) gas at 150 kPa, sot. Now the valve is opened, allowing the two gases to mix with each other. Heat transfer occurs during the mixing process. The final equilibrium temperature is 44'C. The specific heats of monatomic gases are independent of temperature. Determine: (a) the final volume of...
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