# Calculations Involving Specific Heat and Latent Heat of

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1) Temperature and Thermal Energy Key Ideas
Temperature is a measure of the average kinetic energy of each particle within an object.
Three temperature scales are Fahrenheit, Celsius, and Kelvin
Fahrenheit scale – The temperature scale on which 32&deg;F (water freezes) and 212&deg;F (water
boils).
Celsius scale - The temperature scale on which 0&deg;C (water freezes) and 100&deg;C (water
boils).
Kelvin scale - The temperature scale on which zero is the temperature at which no more
energy can be removed from matter. Also known as Absolute zero. Standard 4f There
is no temperature lower than 0 Kelvin
Thermal energy is the total energy of the particles that make up an object
2) The Nature of Heat Key Ideas
 Heat is a transfer of thermal energy from an object at a higher temperature to an object
at a lower temperature.
 Heat is transferred by conduction, convection, and radiation.
 A conductor transfers heat well whereas an insulator does not.
 The amount of heat necessary to raise a given mass of a substance by a specific unit of
temperature is called the specific heat.
q = m(T)Cp where:
q = heat energy
m = mass
T = temp. change
Cp = specific heat
3) Quantifying energy:
 The traditional unit of energy is the calorie (cal), which is the amount of energy you need
to add to 1 gram of water to heat it by 1 C.
 Food is measured in units of 1000 calories called kilocalories (kcal), which is more
commonly known as the Calorie (Cal).
 The metric unit of energy is the joule (J). There are 4.184 J/cal.
 Because a joule isn’t very much energy, we usually measure energy in units of 1000 joules
called kilojoules (kJ).
Key Terms
 Specific heat –is the amount of heat per unit mass required to raise the temperature by one
degree Celsius. The relationship between heat and temperature change is usually expressed in
the form shown where c is the specific heat. The relationship does not apply if a phase
change is encountered, because the heat added or removed during a phase change does
not change the temperature.
The specific heat of Water is Cp (H2O) = 1.00 cal/(gC) = 1.00
cal
J
 4.18
g C
g C
a. How many joules of energy must be absorbed to raise the temperature of 20 grams of water
from 25&deg;C to 30&deg;C?
Type 1. Heat Transferred (q) is the unknown:
Ex. Aluminum has a specific heat of 0.902 J/g x oC. How much heat is lost when a piece of
aluminum with a mass of 23.984 g cools from a temperature of 415.0 oC to a temperature of 22.0
o
C?
Step 1: First read the question and try to understand what they are asking you. Can you picture
a piece of aluminum foil that is taken out of an oven. Imagine the aluminum losing heat to its
surroundings until the temperature goes from 415.0 oC to 22.0 oC.
Step 2: Write the original formula.
q = m(T)Cp
Step 3: List the known and unknown factors. Looking at the units in the word problem will help
you determine which is which.
q=?
m = 23.984 g
DT = (415.0 oC - 22.0 oC) = 393.0 oC (remember, they asked for the change in temperature)
Cp = 0.902 J/g x oC
Step 4. Substitute your values into the formula
q=?
m = 23.984 g
DT = (415.0 oC - 22.0 oC) = 393.0 oC
Cp = 0.902 J/g x oC
q = m(T)Cp
q = 23.984 g x 393.0 oC x 0.902 J/g x oC
Step 5. Cross out units where possible, and solve for unknown.
q = 23.984 g x 393.0 oC x 0.902 J/g x oC
q = 8501.992224 J
Step 6. Round to the correct number of significant digits and check to see that you answer
makes sense.
q = 8.50 x 103 J
Our answer makes sense because joules (J) are acceptable units for q, and the value should be
positive based on the wording of the question.
Example
An 50 gram sample of an unknown metal warms from 18&deg; to 58&deg; after absorbing 800 joules. What
is the specific heat of the metal?
When a substance is changing state, the temperature of the substance remains constant even
though its thermal energy is changing.
Change of state – The physical change of matter from one state to
another.
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Melting – The change from a solid to the liquid form of matter.
Melting point – The temperature at which a substance melts.
Freezing – The change from the liquid to the solid form of matter.
Freezing point – The temperature at which a substance freezes.
Vaporization - The change from the liquid to the gaseous form of matter.
Evaporation – Vaporization that occurs at the surface of a liquid.
Boiling – Vaporization that occurs below the surface of a liquid.
Boiling point – The temperature at which a liquid substance boils.
Condensation – The change from the gaseous to the liquid form of matter.
Freezing and Boiling Point Graph, Vapor Pressure and Boiling, Phase Diagram
http://ess.lamar.edu/people/faculty/pittmanjg/teaching/the-oceans-online-fall-2006/assignments/atmospheric-and-oceanic-circulation/water-phase-changes-cool.jpg
Energy During Change of States1
Heat of Fusion: The energy required to change a gram of a substance
the solid to the liquid state without changing its temperature is
commonly called it's &quot;heat of fusion&quot;. This energy breaks down the
solid bonds, but leaves a significant amount of energy associated
with the intermolecular forces of the liquid state.
The equation is Q = m Hfus
where: Q = energy, m = mass and Hfus = heat of fusion
The Hfus = heat of fusion for water is 80 cal/g = 334 J/g
1
http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/phase2.html#c1
from
Heat of Vaporization: The energy required to change a gram of a liquid into the gaseous state at
the boiling point is called the &quot;heat of vaporization&quot;. This energy breaks down the intermolecular
attractive forces, and also must provide the energy necessary to expand the gas (the PV work
applied). For an ideal gas, there is no longer any potential energy associated with intermolecular
forces. So the internal energy is entirely in the molecular kinetic energy.
The equation is Q = m Hvap
where: Q = energy, m = mass and Hvap = heat of vaporization
The Hvap = heat of vaporation for water is 540 cal/g = 2260 J/g
A significant feature of the vaporization phase change of water is
the large change in volume that accompanies it.
A mole of water is 18 grams, and at STP that mole would occupy
22.4 liters if vaporized into a gas.
If the change is from water to steam at 100&deg;C, rather than 0&deg;C,
then by the ideal gas law that volume is increased by the ratio of
the absolute temperatures, 373K/273K, to 30.6 liters. Comparing
that to the volume of the liquid water, the volume expands by a
factor of 30600/18 = 1700 when vaporized into steam at 100&deg;C.
This
is a physical fact that firefighters know, because the 1700-fold
increase in volume when water is sprayed on a fire or hot surface can be explosive and dangerous.
One way to visualize this large volume change is to note the volume of 18 ml of water in a
graduated cylinder as the volume occupied by Avogadro's number of water molecules in the liquid
state. If converted into steam at 100&deg;C this same mole of water molecules would fill a balloon
38.8 cm in diameter (15.3 inches).
Since heat (energy that’s being transferred through thermal motion) is more important than work
(for our purposes), how do we measure it? More definitions of use:
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System: Whatever we’re studying.
o
This can be practically anything. If we are studying what happens when we heat a
pan on the stove, the pan will be the system we are studying.
o
If a system gets energy added to it, the amount of energy it has after the change
is positive. Because of this, an endothermic process is any process in which energy
is absorbed by the system we’re talking about.
o
If a system has energy taken away from it, the amount of energy it has after the
change is negative. Because of this, an exothermic energy is any process in which
energy is given off by the system we’re talking about.
Surroundings: Everything outside the system.
o
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When studying the pan above, the surroundings will primarily consist of the stove
(because it’s putting energy into the pan), though it technically consists of
everything but the pan.
Universe: The system + the surroundings.
o
In a general sense, the universe consists of everything that exists anywhere. From
a thermodynamic standpoint, the universe usually consists of whatever the system
we’re referring to is as well as whatever is putting energy into or taking energy
away from it.
o
Example: If we’re studying a space heater, the heater will be our system, the
house will be our surroundings, and the universe will be the heater and the house
together (we ignore the irrelevant rest of the world, since it doesn’t really play a
part in anything).
Science Help Online Worksheet 2-10a Heat Transfer Worksheet2
q = m(T)Cp
Use the above formula to solve the problems below. Remember to list the known and unknowns.
1. How many calories of heat are required to raise the temperature of 550 g of water from 12.0 oC to
18.0 oC? (remember the specific heat of water is 1.00 cal/g oC)
2. How much heat is lost when a 640 g piece of copper cools from 375 oC, to 26 oC? (The specific heat
of copper is 0.38452 J/g oC)
3. The specific heat of iron is 0.4494 J/g oC. How much heat is transferred when a 24.7 kg iron ingot
is cooled from 880 oC to 13 oC?
2
http://www.fordhamprep.org/gcurran/sho/sho/worksheets/worksht210a.htm
Calculations Involving Specific Heat and Latent Heat of Phase Change3
Standard: Students know how to solve problems involving heat flow and temperature
changes, using known values of specific heat and latent heat of phase change.
1. The specific heat of carbon (graphite) is 0.71 J/(g&middot;&deg;C). How much energy is given off as a 2
gram piece of graphite cools from 120&deg;C to 20&deg;C?
2. A sample of mercury has a mass of 500 grams. When it absorbs 280 joules, the temperature is
found to have increased from 25&deg;C to 29&deg;C. What is the specific heat of mercury?
3. How much energy must be absorbed by 10 grams of steam in order to raise its temperature by
100&deg;C? The specific heat of steam is 1.87J/(g&middot;&deg;C).
4. A 50 gram piece of iron warms from 0&deg;C to 40&deg;C while absorbing 900 joules. What is the
specific heat of iron?
5. How much energy must be removed from 500 grams of water in order to cool it from 80&deg;C to
40&deg;C? The specific heat of water can be found on your periodic table.
3
http://www.sciencegeek.net/Chemistry/taters/Unit7Thermochemical.htm
6. When a 500 gram piece of brass cools from 100&deg;C to 60&deg;C, it is found to have given up 7600
joules of energy. What is the specific heat of the brass?
7. How much energy is required to melt 4 moles of ice at its melting point? Assume that the molar
heat of fusion of ice is 6 kJ/mol.
8. How much energy is required to boil 4 moles of water at its boiling point? Assume that the
molar heat of vaporization of water is 41 kJ/mol.
9. An engineer wants to be able to condense 10 moles of water vapor every minute. Assuming the
steam is at 100&deg;C, how much energy must be removed every minute? Assume that the molar heat
of vaporization of water is 41 kJ/mol.
10. How much energy must be removed from 30 moles of liquid water at 0&deg;C in order to convert it
to ice? Assume that the molar heat of fusion of ice is 6 kJ/mol.
13. A sample of ice at 0&deg;C melts after absorbing 300 kJ of heat. How many moles of H2O are
contained in the sample? Assume that the molar heat of fusion of ice is 6 kJ/mol.
14. A sample of water at 100&deg;C is converted to steam after absorbing 820 kJ of heat. How many
moles of H2O are contained in the sample? Assume that the molar heat of vaporization of water is
41 kJ/mol.
15. How many joules of energy are needed to melt 54 grams of ice at its melting point? Assume
that the molar heat of fusion of ice is 6 kJ/mol.
16. How many joules of energy are needed to boil 90 grams of water at its boiling point. Assume
that the molar heat of vaporization of water is 41 kJ/mol.
How is it that you can have both water and
ice at 0 C and both water and steam at 100
C? A lot of energy goes into these phase
transitions. Why doesn't it change the
temperature?
If you have steel and wood at 0 C, which feels colder? If
you have steel and wood at 100 C, which feels hotter?
Will hot water freeze into ice cubes faster than cold
water in your freezer?
If you have a cup of coffee which is too hot to drink,
should you add cream to it immediately to cool it or let it
stay black and sit for a while before adding cream? The
object is to get it cool enough to drink in the shortest
possible time.
What is the difference between evaporation and boiling?
If you heat a uniform metal plate with a hole in it, will
the hole get larger or smaller?
Heat flow is normally from a high temperature toward a
low temperature region. How do you manage to cool
your body on a July day when the temperature is 102 F
(compared to 98.6 F normal body temperature)?
Everyone knows that heat flows from a hot area to a cold
area. How then does your refrigerator get it to flow from
the inside of its freezing compartment to the warm
outside, &quot;uphill&quot; for heat?
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