Now suppose we have a sample of another material, this time a solid. Let’s
call it “substance Y.” We carve a chunk of it down until we have a piece of mass
1.0000 g, accurate to five significant figures. Again, we use a laboratory balance
to determine mass. We transfer 1.0000 cal of energy to substance Y. Suppose the
temperature of this solid goes up by 0.80000°C? This material accepts heat
energy in a manner different from either liquid water or substance X. It takes a
little more than 1.0000 cal of heat to raise the temperature of 1.0000 g of this
material by 1.0000°C. Calculating to the allowed number of significant figures,
we can determine that it takes 1.0000/0.80000 = 1.2500 cal to raise the temper-
ature of this material by 1.0000°C.
We’re onto something here: a special property of matter called the specific
heat, defined in units of calories per gram per degree Celsius (cal/g/°C).
Suppose it takes c calories of heat to raise the temperature of exactly 1 g of a
substance by exactly 1°C. For pure liquid water, we already know c = 1 cal/g/°C,
to however many significant figures we want. For substance X above, c = 0.833
cal/g/°C (to three significant figures), and for substance Y above, c = 1.2500
cal/g/°C (to five significant figures). The value of c is the specific heat for the
substance in question.
Alternatively, c can be expressed in kilocalories per kilogram per degree
Celsius (kcal/kg/°C), and the value for any given substance will be the same.
Thus for water, c = 1 kcal/kg/°C, to however many significant figures we want.
For substance X above, c = 0.833 kcal/kg/°C (to three significant figures), and
for substance Y above, c = 1.2500 kcal/kg/°C (to five significant figures).
THE BRITISH THERMAL UNIT (BTU)
In some applications, a completely different unit of heat is used: the British ther-
mal unit (Btu). You’ve heard this unit mentioned in advertisements for furnaces
and air conditioners. If someone talks about Btus literally, in regard to the heat-
ing or cooling capacity of a furnace or air conditioner, that’s an improper use of
the term. They really mean to quote the rate of energy transfer in Btus per hour
(Btu/h), not the total amount of energy transfer in Btus.
The Btu is defined as the amount of heat energy transfer involved when the
temperature of exactly one pound (1 lb) of pure liquid water rises or falls by one
degree Fahrenheit (1°F). Does something seem flawed about this definition? If
you’re uneasy about it, you have a good reason. What is a “pound”? It depends
where you are. How much water weighs 1 lb? On the earth’s surface, it’s approx-
imately 0.454 kg or 454 g. But on Mars it takes about 1.23 kg of liquid water to
weigh 1 lb. In a weightless environment, such as on board a space vessel orbit-
CHAPTER 1 Background Physics
20