132 3 The Second and Third Laws of Thermodynamics: EntropyStep 4: The gas is cooled reversibly at a constant
volume of 15.00 L from 473.15 K to 373.15 K. Step 5:
The gas is compressed reversibly and isothermally
at 373.15 K from a volume of 15.00 L to a volume
of 10.00 L. Step 6: The gas is cooled reversibly
at a constant volume of 10.00 L from 373.15 K to
298.15 K.
b.Repeat the calculation with all steps the same as in part
a except that step 1 is carried out isothermally and
irreversibly with a constant external pressure of
1.000 atm.3.14 A sample of 2.000 mol of nitrogen gas (assume ideal
withCV, m 5 R/2) expands adiabatically and irreversibly
from a volume of 8.000 L and a temperature of 500.0 K
to a volume of 16.000 L against an external pressure
of 1.000 atm. Find the final temperature,∆U,q,w,
and∆Sfor this process. Find the initial and final
pressures.
3.15 A sample of 1.000 mol of helium gas (assumed ideal with
CV, m 3 R/2) expands adiabatically and irreversibly from
a volume of 3.000 L and a temperature of 500. K to a
volume of 10.00 L against a constant external pressure
of 1.000 atm. Find the final temperature,∆U,q,w, and
∆Sfor this process. Compare each quantity with the
corresponding quantity for a reversible adiabatic
expansion to the same final volume.
3.16 The normal boiling temperature of ammonia is− 33 ◦C,
and its enthalpy change of vaporization is 24.65 kJ mol−^1.
The density of the liquid is 0.7710 g mL−^1.
a.Calculateq,w,∆U,∆H,∆S, and∆Ssurrif 1.000 mol
of ammonia is vaporized at− 33 ◦C. Use the ideal gas
equation of state to estimate the volume of the gas and
neglect the volume of the liquid.
b.Repeat the calculations of part a, using the van der
Waals equation of state to find the molar volume
of the gas under these conditions (use successive
approximations or other numerical procedure to solve
the cubic equation) and without neglecting the volume
of the liquid.
3.17 a.Find the change in entropy for the vaporization of
2.000 mol of liquid water at 100◦C and a constant
pressure of 1.000 atm.
b.Find the entropy change for the heating of 2.000 mol
of water vapor at a constant pressure of 1.000 atm
from 100◦Cto200◦C. Use the polynomial represen-
tation in Table A.6 for the heat capacity of water
vapor.
3.18 a.Calculate the entropy change for the isothermal
expansion of 1.000 mol of argon gas (assume ideal)
from a volume of 5.000 L to a volume of 10.000 L.
b.Calculate the entropy change for the isothermal
expansion of 1.000 mol of argon gas (assume ideal)
from a volume of 10.000 L to a volume of 15.000 L.
c.Explain in words why your answer in part b is not the
same as that of part a, although the increase in volume
is the same.
3.19 a.1.000 mol of helium is compressed reversibly and
isothermally from a volume of 100.00 L and a
temperature of 298.15 K to a volume of 50.00 L.
Calculate∆S,q,w, and∆Ufor the process. Calculate
∆Ssurrand∆Suniv.
b.Calculate the final temperature,∆S,q,w,∆U,∆Ssurr,
and∆Sunivif the gas is compressed adiabatically and
reversibly from the same initial state to a final volume
of 50.00 L.
c.The gas is compressed adiabatically and irreversibly
from the same initial state to the same final volume
withPext 1 .000 atm. What can you say about the
final temperature,∆S,q,w,∆U,∆Ssurr, and∆Suniv?
d.The gas is compressed isothermally and irreversibly
from the same initial state to the same final volume
withPext 1 .000 atm. What can you say about∆S,q,
w,∆U,∆Ssurr, and∆Suniv?
3.20 2.000 mol of helium is expanded adiabatically and
irreversibly at a constant external pressure of 1.000 atm
from a volume of 5.000 L and a temperature of 273.15 K to
a volume of 25.000 L. Calculate∆S,∆Ssurr, and∆Suniv.
State any approximations or assumptions.
3.21 a.Calculate the entropy change for the following
reversible process: 2.000 mol of neon (assume ideal
withCV, m 3 R/2) is expanded isothermally at
298.15 K from 2.000 atm pressure to 1.000 atm
pressure and is then heated from 298.15 K to 398.15 K
at a constant pressure of 1.000 atm. Integrate on the
path representing the actual process.
b.Calculate the entropy change for the reversible process
with the same initial and final states as in part a, but in
which the gas is first heated at constant pressure and
then expanded isothermally. Again, integrate on the
path representing the actual process. Compare your
result with that of part a.
c.Calculate the entropy change of the surroundings in
each of the parts a and b.