Question

(a) Calculate the change in entropy of an ideal gas [for which p = nRT/V]

when its volume is doubled at fixed temperature and number of molecules.

(b) Repeat the calculation for a van der Waals gas

[ for which p = nRT/(V–nb) – a (n/V)^2 ]

(c) Give a physical explanation for the difference between the two.

Answer #1

This problem involves solving the ideal gas law. The first three
questions are tied to Problem 1, so refer back to the problem
statement for conditions. Using the ideal gas equation, calculate
the pressure of oxygen gas in a cylinder with a volume of 25.00 L.
The oxygen masses 4.362 kg and room temperature is at 22.5oC. How
many moles of oxygen are there?
2.Using the same values of volume, mass, and room temperature
from Problem 1, calculate the pressure...

Consider the Ideal Gas Law, which states that PV = nRT, where P
is the pressure, V is the volume, T is the temperature, and n is
the number of moles of a gas sample, and R is a constant. (a)
Assume a sample of 1 mole of a gas is in a expandable container
where temperature and pressure are allowed to vary. Solve this
equation for V = f(P,T).
(b) Determine ∂V/dP and interpret the result. In particular,
describe...

Use the master equation for Helmholtz free energy, A,
to determine the change in entropy as a function of volume under
constant temperature conditions (ds/dv) for a van der waals gas

The van der Waals equation of state is (P + a(n/V )^2)(V/n − b)
= RT, where a and b are gas-specific constants. For Hydrogen gas, a
= 2.45 × 10^-2P a · m^6 and b = 26.61 × 10^-6m^3/mol, while for an
ideal gas a = b = 0. (a) Consider trying to measure the ideal gas
constant in a lab from the relation R = P V/(nT), where P, V, n,
and T are all measured parameters. However,...

Calculate the change in entropy for one mole of ideal gas which
expands from an initial volume of 2 L and initial temperature of
500 K to a final volume of 6 L under the following conditions.
P(initial) refers to the pressure when T(initial)= 500K,
V(initial)= 2 L.
a) Irreversible expansion against a constant pressure of
Pinitial/2
b) Irreversible expansion against a vacuum...a 'free
expansion'.
c) Adiabatic irreversible expansion against a constant pressure
of Pfinal
d) Adiabatic reversible expansion

Calculate the total change of entropy for an ideal monatomic gas
expanding from a volume V into a volume 2V via: i) Free expansion
ii) Quasi-static isothermal expansion iii) Quasi-static adiabatic
expansion; iv) Do the results of (iii) surprise you? Comment on
what these results mean in terms of reversible and irreversible
processes.

The ideal gas law
PV=nRT
relates pressure P, volume V, temperature
T, and number of moles of a gas, n. The gas
constant Requals 0.08206 L⋅atm/(K⋅mol) or 8.3145
J/(K⋅mol). The equation can be rearranged as follows to solve for
n:
n=PVRT
This equation is useful when dealing with gaseous reactions
because stoichiometric calculations involve mole ratios.
A)When heated, calcium carbonate decomposes to yield calcium
oxide and carbon dioxide gas via the reaction
CaCO3(s)→CaO(s)+CO2(g)
What is the mass of calcium carbonate...

± Stoichiometric Relationships with Gases
The ideal gas law
PV=nRT
relates pressure P, volume V, temperature
T, and number of moles of a gas, n. The gas
constant Requals 0.08206 L⋅atm/(K⋅mol) or 8.3145
J/(K⋅mol). The equation can be rearranged as follows to solve for
n:
n=PVRT
This equation is useful when dealing with gaseous reactions because
stoichiometric calculations involve mole ratios.
Part A
When heated, calcium carbonate decomposes to yield calcium oxide
and carbon dioxide gas via the reaction
CaCO3(s)→CaO(s)+CO2(g)...

Derive the Sacker-Tetrode Equation which is the entropy
expression for N indistinguishable ideal gas atoms of total energy
U in a container of volume V.

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Calculate the pressure:
a) Using the ideal gas law
b) using the van der Waals equation
c) Explain the reason for the difference
d) Identify which correction (that for P or V) is dominant and
why

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