Physical Chemistry Third Edition

72 2 Work, Heat, and Energy: The First Law of Thermodynamics

Exercise 2.20

Sincedw >−PdVfor an irreversible compression process, show that the final temperature

for an irreversible adiabatic compression of an ideal gas must be higher than the final

temperature of the reversible adiabatic compression with the same initial state and the same final

volume.

PROBLEMS

Section 2.4: Calculation of Amounts of Heat and Energy
Changes

2.23 a.Calculate the Joule coefficient for carbon dioxide at

298.15 K, using the truncated virial equation of state.

ApproximatedB 2 /dTby the quotient of finite

differences of the values for 0◦C and 50◦C. Use the

value ofCP, min Table A.8 to obtain a value ofCV, m.

State any assumptions or approximations.

b.Find the final temperature if 1.000 mol of carbon

dioxide at 298.15 K and 33 atm is expanded into an

evacuated vessel with a volume of 20.00 L.

2.24 A sample of 3.00 mol of argon is heated from 25.00◦Cto
100.00◦C, beginning at a pressure of 1.000 atm
(101,325 Pa).
a.Findq,w, and∆Uif the heating is done at constant
volume.
b.Findq,w, and∆Uif the heating is done at constant
pressure.

2.25 Find the final pressure if 2.000 mol of nitrogen is
expanded adiabatically and reversibly from a volume of
20.00 L to a volume of 40.00 L, beginning at a pressure
of 2.500 atm. Assume nitrogen to be ideal with
CV, m 5 R/2.

2.26 A sample of 1.000 mol of neon gas is expanded from a
volume of 5.000 L and a temperature of 400.0 K to a
volume of 8.000 L.
a.Find the final temperature if the expansion is adiabatic
and reversible. Assume that the gas is ideal and that
CV 3 nR/ 2 constant.
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 1.000 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, starting at the same state as in part a and

ending at the same volume as in part a. State any

assumptions and approximations.

2.27 Find the final temperature and the final volume if

2.000 mol of nitrogen is expanded adiabatically and

reversibly from STP to a pressure of 0.600 atm. Assume

nitrogen to be ideal withCV, m 5 R/2.

2.28 1.000 mol of carbon dioxide is expanded adiabatically

and reversibly from 298.15 K and a molar volume of

5.000 L mol−^1 to a volume of 20.00 L mol−^1.

a.Find the final temperature, assuming the gas to be ideal

withCV, m 5 R/ 2 constant.

b. Find the final temperature, assuming the gas to be

described by the van der Waals equation with

CV, m 5 R/ 2 constant.

2.29A sample of 20.00 g of acetylene, C 2 H 2 , is expanded

reversibly and adiabatically from a temperature of 500 K

and a volume of 25.00 L to a volume of 50.00 L. Use the

value ofCV, mobtained from the value in Table A.8 for

500 K with the assumption that acetylene is an

ideal gas.

a.Find the percent difference between this value ofCV, m

that you obtain and 5R/2.

b. Find the final temperature.

c.Find the values of∆U,q, andwfor the process.

2.30 a.A sample of 2.000 mol of argon gas is adiabatically

and reversibly expanded from a temperature of

453.15 K and a volume of 15.0 L to a final

temperature of 400.0 K. Find the final volume,∆U,