The heat Q that must be
supplied or removed to change
the temperature of a substance
of mass m by an amount ∆T is:
Q = cm∆T
where c is the specific heat
capacity of the substance.
The common unit for
specific heat capacity
is the J/(kg•C°). The
value of specific heat
capacity depends on
the nature of the
material.
Ex. 9 - In a half hour, a 65-kg
jogger can generate 8.0 x 105 J
of heat. This heat is removed
from the jogger’s body by a
variety of means. If the heat
were not removed, how much
would the body temperature
increase? c for the human
body = 3500 J/(kg•C°).
Other than the joule;
the calorie, kilocalorie
and the British thermal
unit are common heat
units. c for water is
1.00 kcal/(kg•C°) or
1.00 cal/(g•C°).
James Joule (1818-1889)
showed that work energy
and heat energy were
related. He showed that
1 kcal = 4186 joules or
1 cal = 4.186 joules.
1 kcal = 4186 joules or
1 cal = 4.186 joules.
This conversion factor
is the mechanical
equivalent of heat.
Ex. 10 - Cold water at 15 °C enters
a heater, and the resulting hot
water has a temperature of 61°C.
A person uses 120 kg of hot water
in taking a shower. (a) Find the
energy needed to heat the water.
(b) Assuming that the power utility
charges $0.10 per kilowatt•hour for
electrical energy, determine the
cost of heating the water.
The value of specific heat
capacity depends on whether
pressure or volume are held
constant. This distinction is
usually not important for
liquids and solids but is
significant for gases.
A calorimeter is an
insulated container
which can be used to
measure heat loss or
gain between materials
contained within.
Ex.11 - A calorimeter cup is made from
0.15 kg of aluminum and contains 0.20
kg of water. Initially, the water and the
cup have a common temp. of 18.0 °C.
An unknown material (m = 0.040 kg) is
heated to a temperature of 97.0 °C and
then added to the water. The temp. of
the water, cup, and unknown is 22.0 °C
after thermal equilibrium. Find the
specific heat capacity of the unknown
material.
Ex.12 - Suppose you are cooking
spaghetti for dinner, and the
instructions say to boil the noodles
in water fro ten minutes. To cook
spaghetti in an open pot with the
least amount of energy, should you
turn up the burner to its fullest so
the water vigorously boils, or
should you turn down the burner
so the water barely boils?
The latent heat is the heat
per kilogram that must be
added or removed when a
substance changes from
one phase to another at a
constant temperature.
The unit is the J/kg.
The latent heat of fusion
Lf refers to a solid to liquid
change. The latent heat of
vaporization Lv refers to a
liquid to gas change.The
latent heat of sublimation
Ls refers to a solid to gas
change.
Ex.13 - Ice at 0°C is placed in
a Styrofoam cup containing 0.32 kg
of lemonade at 27°C. The specific
heat capacity of lemonade is
virtually the same as water.
After the ice and lemonade reach
equilibrium, some ice still remains.
Determine the mass of ice that has
melted.
Ex.14 - A 7.00-kg glass bowl
[c = 840 J/(kg•C°)] contains 16.0 kg of
punch at 25.0 °C. Two-and-a-half kg of
ice [c = 200 J/(kg•C°)] are added to the
punch. The ice has an initial temp. of
-20.0 °C. The punch may be treated as
if it were water [c = 4186 J/(kg•C°)].
When thermal equilibrium is reached,
all the ice has melted, and the final
temperature is above 0 °C. Determine
this temperature.
Under specific conditions, a
substance can exist in equilibrium
in more than one phase at the
same time. If a liquid partially fills a
vacuum, some of the molecules at
the surface will escape the liquid
and form a vapor; the vapor
gathers heat for this change from
collisions with other molecules.
As the number of vapor molecules
increases, more and more return to
the liquid state. Eventually, the
number returning to the liquid state
equals the number changing to the
vapor state. From this time on, the
concentration of vapor does not
change, and the pressure due to
this vapor remains constant.
The pressure of the
vapor that coexists in
equilibrium with the
liquid is the equilibrium
vapor pressure of the
liquid.
Equilibrium vapor pressure
does not depend on the
volume of space available;
it depends only on the
temperature of the liquid;
a higher temperature
results in a higher pressure.
A graph of the equilibrium
pressure vs. the
equilibrium temperature
can be plotted and the
resulting curve is the
vapor pressure curve, or
the vaporization curve.
If water is boiled in an open
container, the pressure of the
water vapor must equal the
air pressure (1.01 x 105 Pa).
On the vaporization
curve of water, this
pressure corresponds to
a temperature of 100°C.
A liquid boils at the
temperature for which its
vapor pressure equals
the external pressure.
Therefore, the boiling point of
water is lower for lower
pressures and higher for
higher pressures.
A solid can also be in
equilibrium with its liquid
phase only at certain specific
conditions of temperature
and pressure. For each
temperature, there is a single
pressure at which solid and
liquid can exist.
A plot of equilibrium
pressure vs.
equilibrium
temperature for solid
and liquid is called
a fusion curve.
The total pressure of
a mixture of gases,
such as air, is the
sum of the partial
pressures of the
component gases.
The partial pressure of a
gas is the pressure it
would exert if it alone
occupied the entire
volume at the same
temperature as the
mixture.
Relative humidity is
the ratio of the partial
pressure of water
vapor in the air to the
equilibrium vapor
pressure at a given
temperature.
Percent relative humidity is equal to
the partial pressure of water vapor
divided by the equilibrium vapor
pressure of water at the existing
temperature multiplied by 100.
The vapor pressure in the air
cannot exceed the value in the
denominator; if it did, it would
condense as dew or rain.
When the partial
pressure equals the
equilibrium vapor
pressure, the relative
humidity is 100%.
The vapor is said
to be saturated.
If air containing water vapor
is cooled, a temperature is
reached where partial
pressure is equal to
equilibrium vapor pressure.
This is called the dew point
and would correspond to a
relative humidity of 100%.
The dew point is the
temperature below which
water vapor in the air will
condense into dew or fog.
Water forms on the outside of
a glass when the temperature
of the air around the glass
cools to below the dew point.