Physical Chemistry Third Edition

52 2 Work, Heat, and Energy: The First Law of Thermodynamics

Thespecific heat(better called thespecific heat capacity) is denoted bycand is

defined as the heat capacity per unit mass,

c

(

C

m

)

(2.2-2)

wheremis the mass of the object. For a pure substance themolar heat capacity

is denoted byCmand is defined as the heat capacity divided by the amount of the

substance measured in moles. We will use both the molar heat capacity at constant

pressure

CP, m

(

CP

n

)

(2.2-3)

and the molar heat capacity at constant volume

CV, m

(

CV

n

)

(2.2-4)

wherenis the amount of the substance in moles. Both of these molar heat capacities

are intensive variables. It is an experimental fact thatthe heat capacity of any object is

always positive. There is no such thing as a system that lowers its temperature when

heat is added to it.

If an object is heated from temperatureT 1 to temperatureT 2 without any chemical

reaction or phase change occurring, the quantity of heat transferred to the object is

given by

q

∫

c

dq

∫T 2

T 1

CdT (2.2-5)

If the heat capacity is independent of temperature

qC

∫T 2

T 1

dTC(T 2 −T 1 )C∆T (ifCis independent ofT) (2.2-6)

A positive value ofqindicates heat transferred to the system and a negative value

indicates heat transferred from the system to its surroundings.

Thecaloriewas the first metric unit of heat and was originally defined as the

amount of heat required to raise the temperature of 1 gram of liquid water by 1◦C

at 15◦C. The specific heat capacity of liquid water equals 1.00 cal K−^1 g−^1 at 15◦C.

The heat capacity of liquid water is nearly temperature-independent and we can use

this value for any temperature with good accuracy. The calorie is now defined to

equal 4.184 J (exactly) so that heat capacities can be expressed in joules as well as in

calories.

EXAMPLE 2.9

a.Find the amount of heat in calories needed to heat 3.20 mol of liquid water from 25.00◦C

to 95.00◦C.

b.The specific heat of aluminum equals 0.215 cal K−^1 g−^1. Find the final temperature if a

piece of aluminum with mass 25.00 g and at an initial temperature of 90.00◦C is placed

in 100.00 g of liquid water initially at 20.00◦C.