Thermal Energy & Thermodynamics

**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 (T_{2} - T_{1}).

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: **m _{w} c_{w} ΔT_{w} = m_{d} c_{d} ΔT_{d} **where

**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 H _{f},** where H

**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: **Δ l = α l ΔT **where

**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 **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**

**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 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.

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 m^{2}

**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) elasticity**. **Stress = F / A **where **F** is the stretching force in Newtons and **A** is the cross sectional area in m^{2}. Stress has the unit N/m^{3}.

**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

METAL | Tensile Strength (x10^{8}) (N/m ^{2}) |
Young's Modulus (x10^{10}) (N/m ^{2}) |

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 |

- 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.
- How much heat is required to raise the temperature of 152 g of Al (c = 903) from 25° C to 154° C?
- What is the specific heat of a substance if 2350 J of heat raises the temperature of a 52 g sample 60° C?
- 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.
- 210 g of Al at 100° C is added to 235 g of water at 12°C. Compute the final temperature of the mixture.
- 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.
- 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.
- 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.
- 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?
- 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?

c_{ice}= 2060

c_{steam }= 2020

c_{water}= 4180

c_{Al}= 906

c_{glass}= 664

Q_{f}for water = 3.34 x 10^{5}

Q_{v }for water =2.26 x 10^{6}

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

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 |

- 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.
- A Cu pipe is 12.0000 m long at 20° C. What is its New length at 250°C?
- A Fe cookie sheet has an area of 0.89000 m
^{2}at 20°C. What is its New area at 200°C? - A Cu pipe is exactly 2.5000 m long at 5.00°C. At what temperature will it be 2.501 m?
- A quantity of methanol occupies 500.000ml at20.0°C. What is its volume at 45.0°C?
- 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?

- The tensile strength of a certain metal is 8.22 x 10
^{8}N/m^{2}. What force will break a wire with XS of 59.22 mm^{2}? - The Young’s modulus of a material is 12.3 x 10
^{10}N/m^{2. }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. - A 8.23 kg mass causes a spring to stretch 15.90 cm. What weight will cause the spring to stretch 17.00 cm?
- A force of 203.2 N stretches a wire with a cross sectional area of 25.22 mm
^{2}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. - A wire with a cross sectional area of 2.89 cm
^{2}has a length of 6.34 m and is composed of a material with a Young’s modulus of 12.2 x 10^{10}N/m^{2}. What force will cause it to stretch0.0948 mm? - 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 = ________m^{2}

Force (N) | Δ l (m x 10^{-4}) |
Stress x 10^{9 }(N/m^{2}) |
Strain x 10^{-4} |

1 | 2.24 | ||

2 | 4.64 | ||

3 | 6.81 | ||

4 | 8.97 | ||

5 | 11.28 |

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

- 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).
- 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?
- A platinum wire has a cross sectional area of 3.20 x 10
^{-3}cm^{2}. What force will break the wire? - 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 cm^{2}, calculate Young's modulus. - How much force is Needed to snap a copper wire with an area of0.0120 mm
^{2}? - A copper wire that is 2.00 m long is suspended from a support. If the XS area of the wire is0.880 mm
^{2}, how much will it stretch when a weight of 200.0 N is suspended from it? - 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.

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