(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.
Homework Answers
Add Answer to:
(a) Show that the entropy of mixing for two volumes of monatomic
ideal gases A and...
Two reservoirs with identical volumes contain different ideal gases. The total masses of the gases are m1 and m2, the temperatures and pressures are equal. When the reservoirs are connected to each o...
Two reservoirs with identical volumes contain different ideal gases. The total masses of the gases are m1 and m2, the temperatures and pressures are equal. When the reservoirs are connected to each other, the gases mix due to diffusion. Find the entropy change during this process, if the molar masses of the gases are known. (2p)
Two reservoirs with identical volumes contain different ideal gases. The total masses of the gases are m1 and m2, the temperatures and pressures are...
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...
2. 10 points Consider a thermally isolated system consisting of two volumes of an ideal gas...
2. 10 points Consider a thermally isolated system consisting of two volumes of an ideal gas separated by a thermally conducting movable partition, which is initially fixed. Initially, the temperatures, pressures, and volumes of the two parts are P, V, T and 3P, 2V, and T respectively (see figure below). The partition is now allowed to move without gases mixing, until the equilibrium is reached. a) What is the change of the internal energy of the system after the equilibrium...
B. Two distinguishable monatomic ideal gases A and B are held in a volume V by...
B. Two distinguishable monatomic ideal gases A and B are held in a volume V by a movable partition of zero weight and volume. The relative proportions of A and B are arbitrary as the system is in equilibrium (i.e., the pressure P and temperature T are uniform throughout the system). Let N = N , +N be the total number of molecules and let x be the fraction of speed or (NB = XN). (a) Calculate the change in...
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.
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)...
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...
Two vessels A and B each contain N molecules of the same ideal monatomic gas at the same pressure P. Initially, the two...
Two vessels A and B each contain N molecules of the same ideal monatomic gas at the same pressure P. Initially, the two vessels are thermally isolated from each other, and have initial temperatures TA and Ta respectively. The two vessels are brought into thermal contact, and reach equilibrium at the same pressure P and the new final temperature 7, 4-2 (a) Calculate an expression for the final temperature in terms of the initial temperatures. [2 marks] (b) Find the...
B.2 The multiplicity of a monatomic ideal gas is given by 2 = f(N)VN U3N/2, where...
B.2 The multiplicity of a monatomic ideal gas is given by 2 = f(N)VN U3N/2, where V is the volume occupied by the gas, U its internal energy, N the number of particles in the gas and f(N) a complicated function of N. [2] (i) Show that the entropy S of this system is given by 3 S = Nkg In V + ŽNkg In U + g(N), where g(N) is some function of N. (ii) Define the temperature T...
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...
Two reservoirs with identical volumes contain different ideal gases. The total masses of the gases are m1 and m2, the temperatures and pressures are equal. When the reservoirs are connected to each other, the gases mix due to diffusion. Find the entropy change during this process, if the molar masses of the gases are known. (2p)
Two reservoirs with identical volumes contain different ideal gases. The total masses of the gases are m1 and m2, the temperatures and pressures are...
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...
2. 10 points Consider a thermally isolated system consisting of two volumes of an ideal gas separated by a thermally conducting movable partition, which is initially fixed. Initially, the temperatures, pressures, and volumes of the two parts are P, V, T and 3P, 2V, and T respectively (see figure below). The partition is now allowed to move without gases mixing, until the equilibrium is reached. a) What is the change of the internal energy of the system after the equilibrium...
B. Two distinguishable monatomic ideal gases A and B are held in a volume V by a movable partition of zero weight and volume. The relative proportions of A and B are arbitrary as the system is in equilibrium (i.e., the pressure P and temperature T are uniform throughout the system). Let N = N , +N be the total number of molecules and let x be the fraction of speed or (NB = XN). (a) Calculate the change in...
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)...
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...
Two vessels A and B each contain N molecules of the same ideal monatomic gas at the same pressure P. Initially, the two vessels are thermally isolated from each other, and have initial temperatures TA and Ta respectively. The two vessels are brought into thermal contact, and reach equilibrium at the same pressure P and the new final temperature 7, 4-2 (a) Calculate an expression for the final temperature in terms of the initial temperatures. [2 marks] (b) Find the...
B.2 The multiplicity of a monatomic ideal gas is given by 2 = f(N)VN U3N/2, where V is the volume occupied by the gas, U its internal energy, N the number of particles in the gas and f(N) a complicated function of N. [2] (i) Show that the entropy S of this system is given by 3 S = Nkg In V + ŽNkg In U + g(N), where g(N) is some function of N. (ii) Define the temperature T...
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...
Most questions answered within 3 hours.
-
Let X be the amount of damage a particular company pays out (in
$) for a...
asked 3 minutes ago -
1. Choose the answer that is closest to the definition of a
significance level
a) If...
asked 1 hour ago -
When light is refracted, on what does the angle of refraction
depend? Select all that apply....
asked 1 hour ago -
A (726) g mass is hung on a spring. As a result the spring
stretches (16.5)...
asked 2 hours ago -
SOLUTION NOT NEEDED ONLY NEED THE ANSWERS, HOMEWORK IS DUE IN 30
MINUTES.
4)Which of the...
asked 2 hours ago -
You will select one card from a standard deck of 52 cards. What
is the probability...
asked 3 hours ago -
50% of the volume of a boat, sailing down the Mississippi (where
the water density ρ...
asked 3 hours ago -
Calculate how many moles of ions are in 1.4 L of 2.9 M KNO2
(aq). Remember...
asked 4 hours ago -
Experiment:
In the experiment: Mix together 74 g. (92 ml.) of n-butyl
alcohol and 120 g....
asked 4 hours ago -
This Python module will be menu driven
and use conditions to check user input in order...
asked 5 hours ago -
Tip Calculator App
For this project, you will create a tip calculator Android
app. The user...
asked 5 hours ago -
A first order chemical reaction has an energy of activation of
90.0 kJ/mol and a rate...
asked 7 hours ago