Physical Chemistry Third Edition

54 2 Work, Heat, and Energy: The First Law of Thermodynamics

Heat Transferred during Phase Changes

When a phase change occurs, heat can be transferred to or from the system without

changing its temperature or its pressure. This heat is sometimes calledlatent heat. The

amount of latent heat per unit mass is characteristic of the substance and the phase

transition. The latent heat of fusion (melting) is denoted by∆fusH. For water at 0◦C

and a constant pressure of 1.000 atm∆fusHequals 79.72 cal g−^1. The latent heat of

vaporization (boiling) is denoted by∆vapH. For water at 100◦C and 1.000 atm∆vapH

equals 539.55 cal g−^1.

EXAMPLE2.11

Find the mass of liquid water that can be brought to 100.0◦C from 25.00◦C by contact with

100.0 g of steam at 100.0◦C.

Solution

Define the steam as subsystem 1, the liquid water as subsystem 2. Assume that the heat

capacity of liquid water can be assumed to be constant and equal to 4.18 J K−^1 g−^1. The heat

lost by subsystem 1 must equal the heat gained by subsystem 2.

∆vapH

(

539 .55 cal g−^1

)( 4 .184 J

1 cal

)

22575 J g−^1

q 1 −(2257.5Jg−^1 )(100.0g)−225750 J

q 2 (4.18JK−^1 g−^1 )m(75.00 K)(314Jg−^1 )m−q 1 225750 J

m

225750 J

314Jg−^1

719 g

PROBLEMS

Section 2.2: Heat

2.10 Calculate the amount of heat required to bring 1.000 mol
of water from solid at 0.0◦C to gas at 100.0◦Cata
constant pressure of 1.000 atm. Calculatewfor the
process.

2.11 Compute the rise in temperature of water if it is brought to
rest after falling over a waterfall 50.0 m high. Assume that
no heat is transferred to the surroundings.

2.12 The normal boiling temperature of ethanol is 78.5◦C, and
its molar enthalpy change of vaporization at this
temperature is 40.3 kJ mol−^1. Findqandwif 3.000 mol of
ethanol are vaporized at 78.5◦C and a constant pressure of
1.000 atm.

2.13 a.If a sample of 2.000 mol of helium gas is isothermally
and reversibly expanded at 298.15 K from a pressure

of 2.500 atm to a pressure of 1.000 atm, find

wandq.

b.If the sample of helium from part a is isothermally and

irreversibly expanded from the same initial state to

the same final state withPext 1 .000 atm, find

wandq.

2.14 Calculateqandwif 2.000 mol of helium is heated

reversibly from a volume of 20.0 L and a temperature of

300.0 K to a volume of 40.0 L and a temperature of

600.0 K. The heating is done in such a way that the

temperature remains proportional to the volume.

2.15 The normal boiling temperature of ethanol is 78.5◦C, and

its molar enthalpy change of vaporization at this

temperature is 40.3 kJ mol−^1. Findqandwif 3.000 mol of

ethanol are reversibly vaporized at 78.5◦C and a constant