Course Outline


Matter and Energy



 

After completing this unit you should be able to:

  • recognize different forms of energy
  • convert between the units joule and calorie
  • use specific heat to relate temperature change to quantity of energy transferred

Matter and Energy

In his textbook published in 1789, Lavoisier included in his list of elements two 'substances' that he didn't know what else to do with, light and caloric (heat).  We now know that heat and light are not matter at all, they are forms of energy, as are such things as mechanical work and electrical potential.  Energy is distinct from matter.  Although it is produced from matter and interacts with it, energy has no mass.  Most physical and chemical processes either require energy or produce energy.  Ice melts when it absorbs heat from its surroundings.  When we burn natural gas, primarily the compound methane, it reacts with oxygen from the air and produces two new substances, carbon dioxide and water, along with energy.  The energy produced in this reaction is used to heat our homes and cook our food.

In general terms, energy is the capacity to do work.  There are two fundamentally different ways that matter can contain energy.  Potential energy is the capacity of matter to do work by virtue of position, state,  or composition, i.e. what and where the matter is.  Kinetic energy is the energy associated with motion, i.e. what the matter is doing.  Another empirical rule called The Law of Conservation of Energy states that energy can not be created or destroyed, only converted from one form into another.  The heat released on burning natural gas, for example, is originally stored in the compound as chemical energy.

Thanks to Einstein, we now know that matter and energy are fundamentally related.  There are some processes in which a very tiny amount of mass (m) can be converted into a vast amount of energy (E), according to the equation E = mc2, where c is the speed of light, 3.00 x 108 m.s-1.  For the physical and chemical changes that we shall consider, however, the separate conservation laws of mass and energy hold to a much higher degree of precision than we can typically measure.

Units of Energy

When we heat a sample of matter, it's temperature increases, but temperature is not energy.  Like mass, the total energy associated with a sample of matter is the sum of the energy of its parts.  Temperature is more like density; for a homogeneous sample we will measure the same value of the temperature in any part of the sample.  We know that some substances, metals for example, are more easily heated than others.  The same amount of energy causes different samples of matter to change temperature by different amounts.  The ability of a sample to be heated by transfer of energy is called its heat capacity, and is the product of the mass of the sample and a physical property commonly called specific heat.

A familiar unit of energy is the calorie (cal).  The Calorie (note the capital C) encountered in nutritional information is actually 1000 calories or 1 kcal.  One calorie was originally defined as the amount of energy required to heat 1 g of water by 1 Celcius degree, making the specific heat of water 1.00 cal/g oC.

The SI unit of energy is the joule (J).  The joule is a derived unit equivalent to kg.m2.s-2 (read as kilogram meter squared per second squared; note the use of the negative exponent).  This unit can be best understood in terms of a simple definition of mechanical work: a force acting through a distance.  The SI unit of force is the newton (N), equivalent to kg.m.s-2 (i.e. mass x acceleration as given by Newton's second law), and 1 J = 1 N.m = 1 kg.m2.s-2.

The calorie is now defined in terms of the joule:        1 cal = 4.184 J exactly,
and the specific heat of water is 4.18 J.g-1.K-1 (to 3 sf., at 20 oC and 1 atm pressure).

Using Specific Heat

Knowing how much energy it takes to heat 1 g of water by 1 C degree (i.e. 1 kelvin), we can calculate the amount of heat used to raise the temperature of any mass of water by any amount using this equation:

heat energy gained (q)  =  mass (m)  x  specific heat (cp)  x  temperature increase (ΔT)

The Greek letter, Δ (capital delta), is often used in science to indicate a difference, in this case between the final temperature and the initial temperature of the water.

Example: How much heat is required to raise the temperature of 25.0 g of water from 17.3 oC to 40.0 oC?

ΔT  =  Tfinal - Tinitial  =  40.0 - 17.3   =   22.7 C degrees  =  22.7 K

q  =  m  x  cp  x  ΔT  =  25.0 g  x  4.18 J.g-1.K-1  x  22.7 K  =  2.37 x 103 J  =  2.37 kJ

Since the amount of heat transferred to water is easily calculated from the temperature change, we can use this simple measurement to determine the heat involved in other physical and chemical processes.  Problem 1 illustrates a general method by which the energy content of food can be determined.  The experimental technique is called calorimetry, and is done in an insulated container so that all of the heat produced by the combustion is used to heat the water rather than being lost to the surroundings.  Problem 2 shows how to determine the specific heat of other substances using the law of conservation of energy.

Problem 1: What is the energy content of a cookie (in Calories) if the energy released from burning it raises the temperature of 3.25 kg of water from 19.2 oC to 42.3 oC?

ΔT  =  Tfinal - Tinitial  =  42.3 - 19.2   =   23.1 C degrees  =  23.1 K

q  =  m  x  cp  x  ΔT  =  3.25 x 103 g  x  4.18 J.g-1.K-1  x  23.1 K  =  3.138 x 105 J

Note that the mass has been expressed in grams so that the units cancel correctly.  Finally we convert the answer to the units requested in the problem, nutritional calories:

Problem 2: A 5.23 g sample of a metal initially at 66.0 oC is added to 7.26 g of water initially at 19.0 oC.  The final temperature of the water and metal is 20.8 oC.  What is the specific heat of the metal?

First we calculate the amount of heat gained by the water.  The subscript w reminds us that the numbers used in this part of the calculation are for the water.

ΔTw  =  (Tfinal - Tinitial)w  =  20.8 - 19.0   =   1.8 C degrees  =  1.8 K

qw  =  mw  x  cpw  x  ΔTw  =  7.26 g  x  4.18 J.g-1.K-1  x  1.8 K  =  54.68 J

The heat gained by the water is the heat lost by the metal (subscript m).  The law of conservation of energy requires that the magnitudes of the two amounts must be the same, but the signs must be different.  By convention, heat gained is positive and heat lost is negative.  Another way of looking at this is to recognize that the total heat gained by all components of the system combined must be zero, or mathematically:

qw  +  qm  =  0

so       qm  =  -qw  =  -54.68 J

The negative sign indicates that heat is lost from the metal.  Because the metal is cooling, Tfinal < Tinitial and ΔT for the metal is also negative.  Substituting these values into a rearranged form of our equation allows us to calculate the specific heat of the metal:

Comparing this value with the reported specific heats of various metals listed in tables allows us to conclude that the metal is probably silver (specific heat = 0.235 J.g-1.K-1 at 25 oC).

 

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