Question

Consider 5.000 mol of neon in a 208.7 cm^3 piston at 120.0 K. If the gas undergoes isometric cooling to one-half of its initial temperature and then undergoes isothermal reversible expansion to four times of its initial volume, (a) compute the work done assuming the gas behaves ideally. Next, (b) compute the work done for the entire process assuming the gas behaves as a van der Waal's gas (a = 0.2050 atmL^2/mol^2, b = 1.670 x 10^-2 L/mol). (c) Compare and explain your results.

Answer #1

a.] work done in isothermal reversible expansion is given as:

w = -nRT ln (Vf/Vi) where Vf = final volume and Vi = initial volume

T = 120/2 = 60 K

Vi = 208.7 cm^3

Vf = 4 X 208.7 cm^3 = 834.8 cm^3

Put in the values in the above equation:

w = -5 mol X 8.314 J / K.mol X 60 K X ln (208.7 cm^3 / 834.8 cm^3)

w = - 2494.2 J X (-1.386)

**w = 3457.695 J**

b.] w = nRT ln [(Vf - nb) / (Vi - nb)] + n^{2}a [(1/Vf)
- (1/Vi)]

w = 5 mol X 0.0821 L atm/K.mol X 60 K X ln[(0.8348 L - 0.0835 L)
/ (0.2087 L - 0.0835 L)] + 5.125 atm.L^{2} [(1.198 L -
4.792 L)]

w = 24.63 L.atm X ln (0.7513 / 0.1252) + 5.125 atm.L^{2}
(-3.594 L^{-1})

w = 44.134 L.atm - 18.42 atm.L

**w = 25.714 L.atm**

Please note that for part B, R used is 0.0821 L.atm / mol.K , all volumes in cm^3 have been converted to L (1 cm^3 = 0.001 L).

Suppose 4.00 mol of an ideal gas undergoes a reversible
isothermal expansion from volume V1 to volume V2 = 8V1 at
temperature T = 300 K. Find (a) the work done by the gas and (b)
the entropy change of the gas. (c) If the expansion is reversible
and adiabatic instead of isothermal, what is the entropy change of
the gas?

7. 1.55 moles of Argon gas undergo an isothermal reversible
expansion from an initial volume of 5.00 L to 105. L at 300 K.
Calculate the work done during this process using: (a) the ideal
gas equation, and (b) the van der Waals equation of state. Van der
Waals parameters for Ar are available in the back of the book.
Compare the two results, what percentage of the work done by the
van der Waals gas arises due to having...

A cylinder of volume 0.320 m3 contains 11.1 mol of
neon gas at 19.1°C. Assume neon behaves as an ideal gas.
(a) What is the pressure of the gas?
Pa
(b) Find the internal energy of the gas.
J
(c) Suppose the gas expands at constant pressure to a volume of
1.000 m3. How much work is done on the gas?
J
(d) What is the temperature of the gas at the new volume?
K
(e) Find the internal energy...

A cylinder of volume 0.290 m3 contains 11.9 mol of
neon gas at 17.3°C. Assume neon behaves as an ideal gas.
(a) What is the pressure of the gas?
Pa
(b) Find the internal energy of the gas.
J
(c) Suppose the gas expands at constant pressure to a volume of
1.000 m3. How much work is done on the gas?
J
(d) What is the temperature of the gas at the new volume?
K
(e) Find the internal energy...

A vessel with a movable piston contains 1.90 mol of an ideal gas
with initial pressure
Pi = 2.03 ✕ 105 Pa,
initial volume
Vi = 1.00 ✕ 10−2
m3,
and initial temperature
Ti = 128 K.
(a) What is the work done on the gas during a constant-pressure
compression, after which the final volume of the gas is 2.50
L?
J
(b) What is the work done on the gas during an isothermal
compression, after which the final pressure...

An ideal gas at 300 K has a volume of 15 L at a pressure of 15
atm. Calculate the:
(1)the ﬁnal volume of the system,
(2) the work done by the system,
(3) the heat entering thesystem,
(4) the change in internal energy when the gas undergoes
a.- A reversible isothermal expansion to a pressure of 10
atm
b.- A reversible adiabatic expansion to a pressure of 10
atm.

A piston pump having a barrel of effective volume 100 cm^3 is
used to exhaust a vessel of volume 2.5x10^3 cm. If the initial
pressure of the air in the vessel is 1 atm, estimate the reduction
in pressure produced by two strokes of the pump, assuming that all
processes are reversible and isothermal and that air behaves as an
ideal gas. Further, estimate the number of strokes needed to reduce
the pressure in the vessel from 1 atm to...

A closed piston-cylinder system contains a 120
moles of neon, a monatomic ideal gas, at pressure
PA = 2.5 atm
and volume VA = 0.80
m3. It undergoes the following cyclic
process:
A -> B: I
There is isothermal expansion to volume double of the original.
B -> C:
Constant-volume process back to its original pressure .
C -> A:
Constant-pressure process back to its initial state
a) Draw a Pressure volume diagram for the cycle. You
don't need to...

a) Calculate delta S(system) for the reversible heating of 1 mol
of ethane from 298K to 1500 K at constant pressure. Use Cp = 5.351
+ 177.669x10-3 T – 687.01x10-7 T ^2 + 8.514x10-9 T ^3 (J/mol K).
Consider the reversible Carnot cycle discussed in class with 1 mol
of an ideal gas with Cv=3/2R as the working substance. The initial
isothermal expansion occurs at the hot reservoir temperature of
Thot=600C from an initial volume of 3.50 L to a...

A 1.79 mol diatomic gas initially at 274 K undergoes this cycle:
It is (1) heated at constant volume to 707 K, (2) then allowed to
expand isothermally to its initial pressure, (3) then compressed at
constant pressure to its initial state. Assuming the gas molecules
neither rotate nor oscillate, find (a) the net energy transferred
as heat to the gas (excluding energy transferred as heat out of the
gas), (b) the net work done by the gas, and (c)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 5 minutes ago

asked 17 minutes ago

asked 29 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 35 minutes ago

asked 48 minutes ago

asked 48 minutes ago

asked 51 minutes ago

asked 51 minutes ago

asked 51 minutes ago