Physical Chemistry Third Edition

2.4 Calculation of Amounts of Heat and Energy Changes 73

w, andqfor the process. Assume argon to be ideal

and assume thatCV, m

3

2

R.

b. Consider an irreversible adiabatic expansion with the

same initial state and the same final volume, carried out

withP(transferred) 1 .000 atm. Find the final

temperature,∆U,w, andqfor this process.

2.31 a.Find the final temperature,∆U,q, andwfor the

reversible adiabatic expansion of O 2 gas from 373.15 K

and a molar volume of 10.00 L to a molar volume of

20.00 L. Assume the gas to be ideal with

CV, m 5 R/2.

b.Repeat the calculation of part a for argon instead of

oxygen. Assume thatCV, m 3 R/ 2.

c.Explain in physical terms why your answers for parts a

and b are as they are.

2.32 a.2.000 mol of O 2 gas is compressed isothermally and
reversibly from a pressure of 1.000 atm and a
temperature of 100.0◦C to a pressure of 3.000 atm. Find
∆U,q,w, and∆Hfor this process. State any
assumptions or approximations. Assume that the gas is
ideal.

b. The same sample is compressed adiabatically and

reversibly from a pressure of 1.000 atm and a

temperature of 100.0◦C to a pressure of 3.000 atm. Find

∆U,q, andwfor this process. State any assumptions or

approximations. Assume thatCV, m 5 RT /2 and that

the gas is ideal.

2.33 For each of the following monatomic gases, calculate the

percent difference between the tabulated value ofCP,min

Table A.8 in the appendix and 5R/2 for each temperature

in the table.

a.Ar

b. H

c.He

d.O

e.C

2.34 For each of the following diatomic gases, calculate the

percent difference between the tabulated value ofCP,min

Table A.8 in the appendix and 7R/2 for each temperature

in the table.

a. CO

b. O 2

c.NO

d.HCl

2.35A sample of 1.000 mol of water vapor originally at 500.0 K

and a volume of 10.0 L is expanded reversibly and

adiabatically to a volume of 20.0 L. Assume that the water

vapor obeys the van der Waals equation of state and that its

heat capacity at constant volume is described by

Eq. (2.4-25) withα 22 .2JK−^1 mol−^1 and

β 10. 3 × 10 −^3 JK−^2 mol−^1.

a. Find the final temperature.

b. Find the value ofwand∆U.

c.Compare your values with those obtained if water

vapor is assumed to be an ideal gas and its heat

capacity at constant pressure is constant and equal to its

value at 500 K.

2.36 a.A sample of 2.000 mol of H 2 gas is reversibly and

isothermally expanded from a volume of 20.00 L to a

volume of 50.00 L at a temperature of 300 K. Findq,w,

and∆Ufor this process.

b.The same sample of H 2 gas is reversibly and

adiabatically (without any transfer of heat) expanded

from a volume of 20.00 L and a temperature of 300 K to

a final volume of 50.00 L. Find the final temperature.

Findq,w, and∆Ufor this process.

2.37A sample of 2.000 mol of N 2 gas is expanded from an

initial pressure of 1.000 atm and an initial temperature

of 450.0 K to a pressure of 0.400 atm.

a. Find the final temperature if the expansion is adiabatic

and reversible. Assume thatCV 5 nR/2, so that

γ 7 / 5  1 .400.

b. Find∆U,q, andwfor the expansion of

part a.

c.Find∆U,q,w, and the final temperature if the

expansion is adiabatic but at a constant external

pressure of 0.400 atm, starting from the same state as in

part a and ending at the same volume as in

part a.

d.Find∆U,q, andwif the expansion is reversible and

isothermal, ending at the same pressure as in

part a.