##### ie-Physics
Thermal Energy & Thermodynamics

### summary and practice

#### Thermal Effects:

Thermal energy is the total energy associated with the motion of the particles in matter.  Thermal energy or heat (Q) is measured in the units of energy (Joules).

Heat can be transported from place to place by radiation, convection, and conduction.

The specific heat (c) of a substance is a measure of the material's ability to absorb and store heat.  (see table 12-1)  Specific heat has the unit J/Kg °C.

The heat required to raise or lower the temperature of an object is computed by using the equation: Q = m c ΔT where m is the mass of the object (measured in kg), c is the specific heat of the substance, and ΔT is the change in the temperature (T2 - T1).

The law of heat exchange states that the heat that is lost by a warm object, w, is equal to the heat that is gained by a colder object, d.  Equation: mw cw ΔTw = md cd ΔTd where m is the mass of the object (measured in kg), c is the specific heat of the substance, and ΔT is the change in the temperature (T2 - T1).

Change of state requires energy.  This energy when put in, breaks bonds or when removed, allows the bonds to form thus effecting a change of state.  The heat involved in the solid-liquid state change is called the latent heat of fusion.  The heat involved in the liquid gas state change is called the latent heat of vaporization.  (see table below)  The heats of fusion and vaporization have the unit of J/Kg

In order to compute the heat required to effect a change of state, the sample must be at the freezing point or boiling point of the substance.  If the sample is Not, heat must be put in (or removed) before the change of state can occur.  See heat required to raise or lower the temperature of an object above.  After the freezing point has been reached, use: Q = m Hf, where Hf is the latent heat of fusion.  After the boiling point has been reached, use: Q = m Hv, where Hv is the latent heat of vaporization.

Thermal expansion and contraction is the change in some dimension of a solid or liquid as a result of a change in the temperature of the material.  In this unit we will consider linear expansion and contraction (changing the length of a solid body).  Equation: Δl = α l ΔT where Δl is the change in the length of the object, l is the original length of the object, ΔT is the change in temperature, and α is the coefficient of linear expansion (see table below). In addition, liquids undergo volume expansion and contraction (changing the volume of the liquid).  Equation: ΔV = β V ΔT where ΔV is the change in the volume of the liquid, β is the coefficient of volume expansion, V is the original volume of the liquid, and ΔT is the change in temperature.

#### Thermodynamics:

Thermodynamics is the Name given to the study of processes in which energy is transferred as heat and work.

Heat is the transfer of energy due to differences in temperature where work is the transfer of energy by other means.

A system is any object or set of objects considered in a thermodynamic calculation.  The remainder of the universe is referred to as the environment.

An open system is one, which allows the transfer of matter and energy to and from the environment.

A closed system only allows the transfer of energy to the environment, but Not matter.  The total matter in a closed system is constant.

An isolated system is a closed system in which there is No energy transfer to the environment whatsoever.

#### The First Law Of Thermodynamics:

The internal energy (U) is the sum total of all the energies associated with the constituent particles in a system.

The first law of thermodynamics is a special case of the law of conservation of energy.  The first law states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work done by the system (W).  ΔU = Q –W

#### Thermodynamic Processes:

Adiabatic processes are processes in which there is Not exchange of heat with the environment (ΔQ = 0).

Isothermal processes are processes in which the temperature remains constant.  If  a gas expands isothermally against a pressure the change in the internal energy is zero and any heat added equals the external work done by the gas.

Isobaric processes are processes in which the pressure of a gas remains constant.

Isochoric processes (isovolumetric) are processes in which the volume of a confined gas in a system remains constant.

#### The Second Law Of Thermodynamics:

The second law of thermodynamics is concerned with the fact that certain processes are irreversible.  This irreversibility points to several statements of the second law.

The Clausius statement: Heat flows Naturally from a hot object to a cold object; heat will Not flow spontaneously from cold objects to hot objects.

The Kelvin-Planck statement: No device is possible whose sole effect is to transform a given amount of heat completely to work.

The entropy statement of the second law is stated two ways: The total entropy (disorder) of a system plus that of its environment always increases as the result of any Natural process.  Natural processes always move toward a state of maximum disorder.  Well-ordered mechanical energy degrades spontaneously to less ordered thermal energy.

Information theory is also concerned with the increase in entropy stated by the second law.  Well-ordered systems contain more information than less ordered ones.  A consequence of the increase of entropy is a corresponding decrease in the information carried by that system.

#### Solids:

The force required to break a rod or wire is called the breaking strength.  The breaking strength of a given rod or wire is independent of its length.  Use the breaking strength equation to compute its value: BS = (TS) (A) where TS is the tensile strength of the material and A is the cross sectional area in m2

Elasticity is that property by virtue of which a body tends to return to its original size or shape after a deformation and when the deforming forces have been removed.

Stress is the force per unit area, which can cause a deformation.  As in the discussion above for thermal effects, here we will only consider longitudinal (lengthwise) elasticityStress = F / A where F is the stretching force in Newtons and A is the cross sectional area in m2.  Stress has the unit N/m3.

Strain is the fractional deformation caused by stress.  Strain = Δl / l where Δl is the elongation and l is the original length.  The strain is a pure number and has no units.

The Modulus of Elasticity is the ratio of Stress/Strain.  It is the slope of the graph of Stress ploted verses Strain, commonly refereed to as Hooke's Law.  The modulus of elasticity for linear elasticity is called Young's modulus.  The equation for Young's modulus is: Y = F l / Δl A.  Where F is the stretching force (in Newtons), l is the original length (in m), Δl is the elongation (in m), and A is the cross sectional area (m2).

#### Tensile Strength And Elastic modulus Of Selected metals

 METAL Tensile Strength  (x108)     (N/m2) Young's Modulus  (x1010)     (N/m2) Al 2.4 6.96 Brass XXX 9.02 Cu 4.8 11.6 Au 2.9 7.85 Fe (hard) 6.9 19.3 Fe (soft) 3.8 9.1 Pb 2.1 1.57 Pt 3.5 16.7 Ag 2.9 7.75 Steel (maximum) 32 20 Steel (minimum) 2.8 20 Tungsten XXX 35.5

#### Thermal Energy Practice Problems

1. 5620 J of heat are applied to a glass (c = 664) mass 45 g. at a temperature of 15°C.  Compute the final temperature of the glass.

2. How much heat is required to raise the temperature of 152 g of Al (c = 903) from 25° C to 154° C?

3. What is the specific heat of a substance if 2350 J of heat raises the temperature of a 52 g sample 60° C?

4. 160 g of water (c = 4180) at a temperature of 85°C is mixed with 220 g of water at 12° C.  Compute the final temperature of the mixture.

5. 210 g of Al at 100° C is added to 235 g of water at 12°C.  Compute the final temperature of the mixture.

6. 108 g of a substance at 100°C is put into 210 g of water at 21° C.  If the final temperature of the mixture is 28° C, compute the specific heat of the substance.

7. 120 g of Pb (c = 190) is raised to a temperature of 120° C is placed into an Al calorimeter cup with a mass of 120 g containing 320 g of water at 10° C.  Compute the final temperature of the mixture.

8. 85 g of an alloy is heated to 110°C and introduced into a 110 g Al calorimeter containing 230 g of water at 12°C.  Compute the specific heat of the alloy if the final temperature of the mixture is 17.5° C.

9. A copper (c=385) mass (452 g) is heated to 140°C and placed into a 250g glass (c=664) beaker containing 500 g water at 15°C.  What is the final temperature of the system?

10. A 235g sample of a metal at 110°C is put into contact with a 500 g block of aluminum at 15°C.  What is the specific heat of the metal if the final temperature of the system is 54°C?

#### Change Of State Problems

cice = 2060
csteam = 2020
cwater = 4180
cAl = 906
cglass = 664
Qf for water = 3.34 x 105
Qv for water =2.26 x 106
1. How much heat is required to convert 450 g of ice at -25° C to water at 74° C?  Express the answer in scientific Notation.

2. How much heat must be removed from 15 g of steam at 100° C to convert it to ice at - 25°C? Express the answer in scientific Notation.

3. A sample of 45 g ice at the freezing point is put into 400 g water at 95°C.  Compute the final temperature.

4. A 12 g sample of steam at 120°C is introduced into a 400 g sample of water at 10°C. Compute the final temperature.

5. A 40 g sample of ice at -12°C is placed into a 230 g glass cup holding 350 g water at 90°C. Compute the final temperature.

6. A 23 g sample of steam at 125°C is introduced into a 200g aluminum cup containing 500g of water at 5°C. Compute the final temperature.

#### Physics Problems On Thermal Expansion And Contraction

 Material Coefficient of linear expansion    (α) ( x 10-6) Coefficient of volume expansion    (β) ( x 10-6) Aluminum 23.8 XXX Iron 12.1 XXX Glass 8.97 XXX Pyrex glass 3.3 XXX Platinum 8.99 XXX Copper 16.8 XXX Methanol XXX 1100 Gasoline XXX 108 Mercury XXX 182 Water XXX 207 Carbon tetrachloride XXX 1236
1. A bar of Al with a length of 3.2000 m at 13° C is heated to 230° C.  Compute the change in its length.

2. A Cu pipe is 12.0000 m long at 20° C.  What is its New length at 250°C?

3. A  Fe cookie sheet has an area of 0.89000 m2 at 20°C.  What is its New area at 200°C?

4. A Cu pipe is exactly 2.5000 m long at 5.00°C.  At what temperature will it be 2.501 m?

5. A quantity of methanol occupies 500.000ml at20.0°C.  What is its volume at 45.0°C?

6. A 2.00 liter Al pot is filled to the very top with water at 20.00°C.  How much water will overflow at 99.000C?

#### Physics Problems On Solids

1. The tensile strength of a certain metal is 8.22 x 108 N/m2.  What force will break a wire with XS of 59.22 mm2?

2. The Young’s modulus of a material is 12.3 x 1010 N/m2.  A wire with a diameter of 2.56 mmhas a length of 2.58 m is subjected to a stretching force of 135 N.  Compute the change in the length of the wire.

3. A 8.23 kg mass causes a spring to stretch 15.90 cm.  What weight will cause the spring to stretch 17.00 cm?

4. A force of 203.2 N stretches a wire with a cross sectional area of 25.22 mm2 and an original length of 3.055 m.  If the elongation of the wire as a result is 2.814 mm, compute Young’s modulus.

5. A wire with a cross sectional area of 2.89 cm2 has a length of 6.34 m and is composed of a material with a Young’s modulus of 12.2 x 1010 N/m2.  What force will cause it to stretch0.0948 mm?

6. An Al wire 2.000m long and0.0400mm in diameter is attached to a support and subjected to successive 1N stretching forces.  The resulting increases in length are recorded in the following data table.  Complete the data table and plot stress as the ordinates and strain as the abscissas. After the points are plotted, draw a best-fit straight line.  Compute the slope of the line, this represents the Young’s modulus for Al. Hint: for ease of graphing, express all of the stresses as 10

L = 2.000 m
d = 0.0400 mm
xs area = ________m2

 Force (N) Δ l  (m x 10-4) Stress x 109  (N/m2) Strain x 10-4 1 2.24 2 4.64 3 6.81 4 8.97 5 11.28

#### Practice Problems - Solids

Use the values for tensile strength and Young's modulus from the previous problem sheet.

1. A 45.0 kg diver on the end of a diving board depresses it 3.67 cm below its unloaded position.  How far will a diver weighing 648 N depress the board (Hooke's law).

2. The spring in a scale with No weight hanging from it is 12.0 cm long.  A 7.50 kg masses stretches the spring to 17.0 cm.  How long will the spring be with a 4.50 kg mass hanging from it?

3. A platinum wire has a cross sectional area of 3.20 x 10-3 cm2.  What force will break the wire?

4. A weight of 2.50 N stretches a 4.30 m wire by 1.19 x 10-3 cm.  If the XS area of the wire is0.100 cm2, calculate Young's modulus.

5. How much force is Needed to snap a copper wire with an area of0.0120 mm2?

6. A copper wire that is 2.00 m long is suspended from a support.  If the XS area of the wire is0.880 mm2, how much will it stretch when a weight of 200.0 N is suspended from it?

7. A brass wire that is 2.57 m long and 2.00 mmin diameter is suspended from the ceiling of the physics laboratory.  An 8.25 kg stool is hung from the wire and causes it to stretch.  Compute the elongation of the wire.

created and © 2002 by William Dietsch
posted & edited 5 February 2008 by D Trapp