Physical Chemistry Third Edition

102 2 Work, Heat, and Energy: The First Law of Thermodynamics

wherePis the pressure andVis the volume of the system. At constant pressure,∆H

is equal toqfor a simple system. Various calculations of∆Hvalues were carried out,

including∆Hvalues for temperature changes, phase changes, and chemical reactions.

ADDITIONAL PROBLEMS

2.66 a.Calculateq,w,∆U, and∆Hif 100.0 g of water is
vaporized at 100.0◦C and 1.000 atm. Assume that the
water vapor is described by the van der Waals equation
of state and that the density of the liquid is
1.00 g cm−^1.
b.Repeat the calculation assuming gas ideality and
neglecting the volume of the liquid compared with that
of the vapor. How usable do you think this
approximation is?

2.67 It is shown in the theory of hydrodynamics^8 that the speed
of sound in a fluid,vs, is given by

v^2 s

VmCP

MκTCV



Vmγ

MκT

whereκTis the isothermal compressibility,Vmis the molar

volume, andMis the molar mass.

a.Find the speed of sound in air at 298.15 K and

1.000 atm, assuming a mean molar mass of

0.029 kg mol−^1 andCV, m 5 R/2.

b.Find the speed of sound in helium at 298.15 K and

1.000 atm.

c.The speed of sound in ethane at 10◦C is equal to

308ms−^1. Find the ratioCP/CVfor ethane at this

temperature.

2.68 A sample of 1.000 mol of N 2 gas is expanded adiabatically
from a volume of 10.00 L and a temperature of 400.0 K to
a volume of 20.00 L. Assume that N 2 is ideal, with
CV, m 5 R/2.
a.Find the final temperature if the expansion is carried
out reversibly.
b.Find the final temperature if the expansion is carried
out with a constant external pressure of 1.000 atm.
c.Find the final temperature if the gas expands into a
vacuum.
d.Find∆Uandwfor each of the processes of parts a, b,
and c.

(^8) H. Lamb,Hydrodynamics, 6th ed., Cambridge University Press,
New York, 1932.
e.For the reversible expansion of part a, show that if the
integral
wrev−
∫
c
PdV
is carried out using Eq. (2.4-27) the same value ofwis
obtained as from
w∆U−q∆U
2.69 a.The pressure on a sample of 1.000 mol of liquid water
is increased from 1.00 bar to 100.00 bar at a constant
temperature of 20.00◦C. Find∆H,∆U,q, andw. State
any assumptions.
b.The pressure on the same sample of water is increased
adiabatically from 1.00 bar to 100.00 bar, beginning at
20.00◦C. Find∆H,∆U,q, andw. State any
assumptions.
2.70Assume that 1.000 mol of octane, C 8 H 18 , is completely
combusted with the stoichiometric amount of oxygen.
Assume that the reaction goes to completion.
a.Assume that the reaction takes place at a constant
temperature of 298.15 K under standard conditions,
with liquid water as one of the products. Find the
values of∆H,∆U,q, andw.
b.Assume that part of the energy of reaction is used to raise
the products of the reaction by 100.0 m near the surface
of the earth. Find the values of∆H,∆U,q, andw.
c.Assume that the reaction is carried out adiabatically and
at constant pressure starting at 298.15 K. Find the final
temperature of the products. If the final temperature is
above 100◦C, the water will be in the form of water
vapor.
2.71 Label the following statements as true or false. If a
statement is true only under certain conditions, label it as
false.
a.If a process is carried out at constant pressure,dq
behaves like an exact differential.
b.Althoughdwis an inexact differential,dwrevis exact.
c.dw−PdVis correct for all simple systems.