Physical Chemistry Third Edition

60 2 Work, Heat, and Energy: The First Law of Thermodynamics

PROBLEMS

Section 2.3: Internal Energy: The First Law of
Thermodynamics

2.17 According to special relativity, the total energy of a system
is given by
Emc^2

wheremis the mass of the system andcis the speed of

light.

a.Assuming a substance with a molar mass of

0.100 kg mol−^1 , calculate the amount of energy

necessary to change the molar mass from its rest-mass

value to a value larger by 1.0 ppm (part per

million).

b.Compare this energy with a typical chemical bond

energy, roughly 400 kJ mol−^1.

c.If the energy in part a were all kinetic energy of the

center of mass of the system, calculate the speed of the

center of mass of the system of 1.000 mol.

2.18 a.Calculateq,w, and∆Uif 2.000 mol of neon (assumed

ideal) is heated at a constant pressure of 1.000 atm

from a temperature of 0.00◦C to a temperature of

250.00◦C.

b.Calculateq,w, and∆Uif the same sample of neon is

heated at a constant volume from the same initial state

to 250.00◦C and is then expanded isothermally to the

same final volume as in part a.

2.19Calculateq,w, and∆Ufor melting 100.0 g of ice at 0.0◦C

and a constant pressure of 1.000 atm. The density of ice is

0.916 g mL−^1.

2.20Calculateq,w, and∆Ufor vaporizing 2.000 mol of liquid

water at 100.0◦C to steam at 100.0◦C at a constant pressure

of 1.000 atm.

2.21Consider the following three processes: (1) A sample of

2.000 mol of helium gas is isothermally and reversibly

expanded from a volume of 10.00 L and a temperature of

400.0 K to a volume of 40.00 L. (2) The same sample is

reversibly cooled at a constant volume of 10.00 L from

400.0 K to a temperature of 300.0 K, then expanded

reversibly and isothermally to a volume of 40.00 L, and

then heated reversibly from 300.0 K to 400.0 K at a

constant volume of 40.00 L. (3) The same sample is

expanded irreversibly and isothermally at a temperature of

400.0 K from a volume of 10.00 L to a volume of 40.00 L

with a constant external pressure of 1.000 atm. Calculate

∆U,q, andwfor each process.

2.221.000 kg of water is pressurized isothermally at 298.15 K

from a pressure of 1.000 atm to a pressure of 10.00 atm.

Calculatewfor this process. State any

assumptions.

2.4 Calculation of Amounts of Heat and Energy

Changes

Like work, heat is not a state function. The amount of heat put into a system can depend

on the path taken from the initial to the final state, as was the case with work.

Exercise 2.7

Show that if

dUdw+dq

and ifdUis an exact differential and ifdwis an inexact differential thendqmust be an inexact

differential.