Physical Chemistry Third Edition

2.4 Calculation of Amounts of Heat and Energy Changes 71

Exercise 2.18

a.Using Eq. (2.4-27) find the final pressure for the adiabatic expansion of Example 2.17. Use

the ideal gas law to find the initial pressure.

b.Use the ideal gas law and the final temperature from Example 2.17 to find the final

pressure.

Irreversible Adiabatic Processes

We have assumed that we can equate P(transmitted) and Pext for a relatively

slow irreversible expansion processes. As an example, consider the expansion of

Example 2.17 if it occurs irreversibly with a constant external pressure.

EXAMPLE2.21

A system consisting of 2.000 mol of argon expands adiabatically and irreversibly from a

volume of 5.000 L and a temperature of 373.15 K to a volume of 20.00 L at a constant

Pext 1 .000 atm. Find the final temperature, assuming thatP(transferred)Pext. Assume

argon to be ideal withCV 3 nR/2.

Solution

w−Pext

∫

dV−Pext∆V

( 1 .000 atm)

(

101325 Pa atm−^1

)

( 15 .00 L)

(

0 .001 m^3 L−^1

)

1520 J

∆Uw−1520 J

∆T

∆U

CV



−1520 J

( 1. 5 )( 1 .000 mol)

(

8 .3145 J K−^1 mol−^1

) 121 .9K

Tfinal 373 .15 K− 121 .9K 251 .3K

This final temperature is higher than the temperature reached reversibly, and this will always

be the case.

Exercise 2.19

For an irreversible adiabatic expansion of 5.00 mol of neon from an initial temperature of 500.0K

and an initial volume of 50.00 L to a final volume of 100.00 L, find the final temperature,∆U,

andwifP(transferred) 1 .000 atm. Compare with the values for a reversible expansion from

the same initial state to the same final volume.

We cannot equatePextandP(transmitted) orPandP(transmitted) for an irreversible

compression, but we can assert thatP(transmitted) will be greater thanP. We will not

attempt calculations for irreversible adiabatic compressions.