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**TOPIC 5: THERMAL EXPANSION**

**Thermal Energy**

The Concept of Heat

Explain the concept of heat

Heat energy (thermal energy) is the form of energy that causes the vibration of the particles of a substance. The more the vibrations the more the heat energy contained.

Changes in the amount of heat energy contained in the substance cause changes in the temperature of the substance.

Temperature – Is the degree of hotness or coldness of a body.

SI Unit of Heat is Joule (J)

The amount of heat content depends on the mass of the body, specific heat capacity and the change in temperature and is mathematically obtained as;

Source of Thermal Energy in Everyday Life

State the source of thermal energy in everyday life

Difference between Heat and Temperature

Distinguish between heat and temperature

**Heat**and

**temperature**are related and often confused. More heat usually means a higher temperature.

**Heat**is energy. It is the total amount of energy (both kinetic and potential) possessed by the molecules in a piece of matter. Heat is measured in Joules.

**Temperature**is not energy. It relates to the average (kinetic) energy of microscopic motions of a single particle in the system per degree of freedom. It is measured in Kelvin (K), Celsius (C) or Fahrenheit (F).

When you heat a substance, either of two things can happen: the temperature of the substance can rise or the state of substance can change.

Heat | Temperature | |
---|---|---|

Definition | Heat is energy that is transferred from one body to another as the result of a difference in temperature. | Temperature is a measure of hotness or coldness expressed in terms of any of several arbitrary scales like Celsius and Fahrenheit. |

Symbol | Q | T |

Unit | Joules | Kelvin, Celsius or Fahrenheit |

SI unit | Joule | Kelvin |

Particles | Heat is a measure of how many atoms there are in a substance multiplied by how much energy each atom possesses. | Temperature is related to how fast the atoms within a substance are moving. The ‘temperature’ of an object is like the water level – it determines the direction in which ‘heat’ will flow. |

Ability to do work | Heat has the ability to do work. | Temperature can only be used to measure the degree of hea |

**Thermal Expansion of Solids**

Expansion of Solids

Demonstrate expansion of solids

When a solid is heated one or more of the following may occur:

- Its temperature may rise
- Its state may change
- It may expand

Expansion of solids is the increase in dimensions of a solid when heated.

Contraction of solids is the decrease in dimensions of a solid when is cooled.

Cooling is simply the process of removing heat from the substance.

**DEMONSTRATION OF EXPANSION OF SOLIDS**

In order to demonstrate the expansion of solid we can use following method

- The ball and Ring Experiment
- The Bar and Gap Experiment

Here we are going to explain about the Ball and Ring experiment.

The Ball and Ring Experiment

**1**When the ball is not heated then it will pass through the ring very easily because it has a small volume.

^{st}Case:
2

^{nd}Case: When the ball is heated, it will expand and increase in volume, so it will not pass through the ring.**The Bar and Gap experiment**

**1**When the Bar not heated (Not raised with temperature) then the dimension will remain constant.

^{st}Case:**2**When the Bar is heated (raised with temperature) then the dimension of the Bar will increase and eventually will not pass thought the Gap.

^{nd}Case:
Expansion of Solids in terms of Kinetic Theory of Matter

Explain expansion of solids in terms of kinetic theory of matter

When a

**solid**is heated, its atoms vibrate faster about their fixed points. The relative increase in the size of solids when heated is therefore small. Metal railway tracks have small gaps so that when the sun heats them, the tracks expand into these gaps and don’t buckle.**Forces due toexpansion**

Normally Expansion and contraction is accompanied by tremendous forces; The presence of force indicates the expansion and contraction is resisted.

Bar breaker

- Consists a strong metal blocker with a pair of vertical jaws J and a strong metal Bar R. The metal bar has a wing nut N at one end and an eye at the other end.
- The bar is placed between the two pair of Jaws
- A short cast iron C is inserted in the eye of the bar.
- The bar is then heated it expands and the wing not screwed to tighten the bar R against the jaws.
- The bar is then allowed to cool as it cools, it contracts the short cast Iron rod C which presses against the jaws of the bar breaker, Resists the contraction of the Metal bar R.
- The resistance to the contraction of the bar sets up very large forces which breaks the short cast Iron rod C in the eye of metal bar, Because the contracting bar is trying to pull itself through the small gap in the frame.

Expansivity of Different Solids

Identify expansivity of different solids

**The coefficient of linear expansion or linear expansivity**

The amount by which the linear dimension of a given solid expands depends on:

- The length of the solid
- The temperature to which the solid is heated
- The nature of solid

Coefficient of linear Expansivity is the fractional increase in length of the solids per original length per degree rise in temperature.

Mathematical formula

SI Unit of coefficient of linear expansion is per degree centigrade (ÂºC

^{-1}) or per Kelvin (K^{-1}).
Example 1

A copper rod has a length of 40cm on a day when the temperature of the room is 22.3ÂºC. What will be its length become on a day when the temperature of the room is 30ÂºC ? The linear expansivity of copper is 0. 000017/ÂºC

Solution

Substance | Linear Expasivity (PerÂºC) |

Aluminum (Al) | 0.000026 |

Brass | 0.000019 |

Copper | 0.000017 |

Iron | 0.000012 |

Steel | 0.000012 |

Concrete | 0.000011 |

Glass | 0.0000085 |

Invar ( Alloy of Iron and Nickel) | 0.000001 |

The Application of Expansion of Solids in Daily Life

Explain the applications of expansion of solids in daily life

**Thermal Expansion of Liquids**

The Apparent Expansion of Liquids

Explain the apparent expansion of liquids

Demonstrate the Effects of Heat on Liquids

Demonstrate the effect of heat on liquids

Liquids unlike solids can be poured. If a liquid is poured into a vessel, it takes the shape of the vessel. For this reason a liquid can't have linear and aerial expansivity, thus liquids have only volume expansivity. Liquids molecules have kinetic energy. This energy increases if the temperature of the liquid is raised by heating. Heating causes the molecules of liquid to move faster.

Activity 1

Items Needed

- Large heat safe glass bowl
- Cooking Oil
- Food Coloring
- Two 2×4 blocks
- Candle
- Match or Lighter

Instructions

- Begin by filling a large glass bowl with cooking oil.
- Next, add between 5-10 drops of food coloring into the oil. Helpful Tip: Place the drops near the center of the bowl.
- Prop the bowl up off the table using two 2×4 blocks.
- Light a candle and carefully place it under the bowl. The flame of the candle should touch the bottom of the glass bowl.
- Look through the side of the glass bowl and watch carefully to observe what happens. Helpful Tip: It will likely take 5 minutes before you see anything happen to the liquid/food coloring.

You can alternatively follow the experiment through the following vedio

Verification of Anomalous of Water

Verify the anomalous expansion of water

The instrument used to demonstrate anomalous expansion of water is called Hope's apparatus. It consists of a brass cylinder, jacket with a mixture of ice and salt and two thermometers at regular intervals upward and at the bottom. The Hope's experiment shows that water contracts as it cools down to 4

^{0}C and then expands as it cooled further below 4^{0}C.
In the year 1805, the scientist T. C. Hope devised a simple arrangement, known as Hope’s apparatus, to demonstrate the anomalous behaviour of water.

Hope’s apparatus consists of a long cylindrical jar with two openings on the side, one near the top and the other near the bottom to fit thermometers in each of these openings. A metallic cylindrical air-tight trough with an outlet is also fitted onto the jar, on its central portion. Two thermometers are fitted air-tight in the two openings of the cylindrical jar. The thermometer near the bottom of the jar is T

_{1}, and the one near the top of the jar is T_{2}. Now the cylindrical jar is filled with water. The cylindrical trough at the central portion of the jar is filled with a freezing mixture of ice and common salt.
The Application of Expansion of Liquids in Everyday Life

Explain the applications of expansion of liquids in everyday life

**Thermal Expansion of Gases**

The Concept of Thermal Expansion of Gases

Explain the concept of thermal expansion of gases

The Relationship between Volume and Temperature of Fixed Mass of Air at Constant Pressure

Investigate the relationship between volume and temperature of fixed mass of air at constant pressure

Three properties are important when studying the expansion of gases. These are; pressure, volume and temperature. Charles' law states that "the volume of a fixed mass of gas is directly proportional to the absolute (Kelvin) temperature provided the pressure remains constant." Mathematically, V

_{1}T_{2}= V_{2}T_{1}.
Example 2

The volume of gas at the start is recorded as 30cm

^{3}with a temperature of 30°C. The cylinder is heated further till the thermometer records 60°C. What is the volume of gas?
Solution:

We know,V/T = constant

therefore,

V

_{1}/T_{1}=V_{2}/T_{2}
V

_{1}=30 cm^{3}
T1 =30°C = 30+273 = 303K

*(remember to convert from Celsius to Kelvin)*
T2 =60°C = 60+273 = 333K

V2 =?

V1/T1=V2/T2

V

_{2}=V_{1}xT_{2}/T_{1}
V

_{2}=30x333/303
= 32.97 cm

^{3}
The Relationship between Pressure and Volume of a Fixed Mass of Air at Constant Temperature

Investigate the relationship between pressure and volume of a fixed mass of air at constant temperature

The relationship obtained when the temperature of a gas is held constant while the volume and pressure are varied is known as Boyle’s law. Mathematically, P

_{1}V_{1}= P_{2}V_{2}. Boyle's law states that the volume of a fixed mass of gas is inversely proportional to its pressure if the temperature is kept constant.
PressurexVolume = constant

PxV = constant

Example 3

The volume of gas at the start is 50 cm

^{3}with a pressure of 1.2 x 10^{5}Pascals. The piston is pushed slowly into the syringe until the pressure on the gauge reads 2.0 x 10^{5}Pascals. What is the volume of gas?**Solution:**

We know

P x V = constant

Therefore,

P

_{1}xV_{1}=P_{2}xV_{2}
P

_{1}=1.2 x 10^{5}^{}Pascals
V

_{1}=50 cm^{3}
P

_{2}=2.0 x 10^{5}Pascals
V

_{2}=?
P

_{1}xV_{1}=P_{2}xV_{2}
V

_{2}=P_{1}xV_{1}/p_{2}
V

_{2}=(1.2x10^{5}x50)/(2.0 x 10^{5})
V

_{2}= 30 cm^{3}
The Relationship between Pressure and Temperature of a Fixed Mass of Air at Constant Volume

Investigate the relationship between pressure and temperature of a fixed mass of air at constant volume

To investigate the relationship between the pressure and the temperature of a fixed mass, the volume of the gas is kept constant. The pressure is then measured as the temperature is varied. P

_{1}/T_{1}= P_{2}/T_{2},this is called pressure law. The pressure law states that "the pressure of a fixed mass of a gas is directly proportional to the absolute temperature if the volume is kept constant".
Example 4

Pressure of gas is recorded as 1.0 x 10

^{5}N/m^{2}at a temperature of 0^{°}C. The cylinder is heated further till the thermometer records 150^{°}C. What is the pressure of the gas?
Solution:

We know, P/T = constant

Therefore,

P

_{1}/T_{1}=P_{2}_{}/T_{2}
P

_{1}=1.0 x 10^{5}N/m^{2}
T

_{1}=0^{°}C = 0+273 = 273K*(remember to convert from Celsius to Kelvin)*
T

_{2}=150^{°}C = 150+273 = 423K
P

_{2}=?
P

_{1}/T_{1}= P_{2}/T_{2}
p

_{2}=p_{1}xT_{2}/T_{1}
p

_{2}=1.0x10^{5}x423/273
= 1.54 x 10

^{5}N/m^{2}
The General Gas Equation from the Gas Laws

Identify the general gas equation from the gas laws

The three gas laws give the following equations:

- pV =
**constant***(when T is kept constant)* - V/T =
**constant***(when p is kept constant)* - P/T=
**constant***(when V is kept constant)*

These 3 equations are combined to give the ideal gas equation:

*Where,*

*p = the pressure of the gas**V = the volume the gas occupies**T = the gas temperature on the Kelvin scale*

From this equation we know that if a fix mass of gas has starting values of p1, V1 and T1, and then some time later has value p2, V2 and T2, the equation can be written as:

Exercise 1

Sabah pumps up her front bicycle tyre to 1.7 x 105Pa. The volume of air in the tyre at this pressure is 300 cm3. She takes her bike for a long ride during which the temperature of the air in the tyre increases from 20°C to 30°C. Calculate the new front tyre pressure assuming the tyre had no leaks and so the volume remained constant?

Absolute Scale of Temperature

Explain absolute scale of temperature

Convertion of Temperature in Degrees Centigrade (Celsius) to Kelvin

Convert temperature in degrees centigrade (celsius) to kelvin

The Kelvin temperature scale takes its name after Lord Kelvin who developed it in the mid 1800s. It takes absolute zero as the starting point and temperature measurements are given the symbol K (which stands for "Kelvin"). Temperature differences on the Kelvin scale are no different to those on the Celsius (°C) scale. The two scales differ in their starting points. Thus, 0°C is 273K.

Converting from Celsius to Kelvin

- Temperature in °C + 273 = Temperature in K

Converting from Kelvin to Celsius

- Temperature in K – 273 = Temperature in °C

Example 5

The temperature of a gas is 65 degrees Celsius. Change it to the kelvin scale.

**Solution**

T(K) = degrees Celsius + 273, T(K) = 65+273

therefore T(K) = 338 K.

Standard Temperature and Pressure (S.T.P)

Explain standard temperature and pressure (S.T.P)

Expansion of Gas in Daily Life

Apply expansion of gas in daily life

Exellent

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