Heat, temperature, and thermal expansion

Introduction

• If the volume of the objects increases due to an increase in temperature, then it is known as thermal expansion.
• The change that occurs in volume, area, or length of an object, is called thermal expansion.
• In the case of a solid, linear expansion is more common.
• The expansion may be an increase in height, length, or thickness in all solids, liquids, and gases.
• Volumetric expansion is more common in liquid and gases.
• The binding forces are different in different materials, and it has a different expansion coefficient.
• If the object has a well structural configuration, its expansion coefficient will be uniform throughout the objects.
• If the object does not have a uniform structural configuration, then it has a different coefficient of expansion(CTE).
• Temperature increase leads to change in shape. Hence the CTE increases.
• Softer metals have higher CTE.
• Harder materials like tungsten have lower CTE.

TYPES OF THERMAL EXPANSION

There are three types of thermal expansion

1. linear expansion
2. area expansion
3. volume expansion

LINEAR EXPANSION

In solid, thermal expansion takes place in the form of an increase in length. For example, if we consider the rod of length l to increase due to increased temperature. The linear expansion is given by

 ΔL = 𝛼L ΔT Lwhere,

• ΔL illustrates the difference in length 
• L is defined as the linear coefficient of thermal expansion
• In the CGS unit, the linear coefficient is represented by celsius.
• In the SI unit, the linear coefficient ‘a’ is represented by kelvin.

VOLUME EXPANSION

The volume of the solid increases due to an increase in temperature. ∆t gives a change in temperature, while a change in volume is given by ∆v = vy∆t.y Here, the coefficient of volume expansion is represented by ‘y’. 

It is also given a ∆VV0=V∆T

• V0 represents original volume,
• V represents expanded volume,
• αv represent volume expansion coefficient,
• ΔT represents temperature difference,
• ΔV represents the change in volume after expansion

AREA EXPANSION

On heating, the area of the solid gets increased.

• A0 is the area of the solid at 0℃ and
• at t0c, the area is given as A0 (l + βt), where β is called superficial expansion. 
• superficial expansion is represented by the unit C-1 or K-1

Here is the relationship between linear, area, and volume expansion 6𝛼 = 3β = 2γ, where

• α as the linear expansion
• β as the area expansion
• γ as the volume expansion

The common formula of the area expansion is given as ∆AA0=A∆T

• A represent original area,
• ΔA represents a change in the area,
• αA represent area expansion coefficient,
• ΔT represents temperature difference,
• A0 represents an expanded area.

For example

Q1) A rod of length 15m heated to 60°C. Suppose the length increases to 20 m after some time. Find the expansion coefficient of the rod. The room temperature is 35°C.

Solution:

Given:

Initial length L0 = 15 m,

Expanded length L = 20 m

Change in length ΔL = 20 – 15 = 5 m

Temperature difference ΔT = 60°C – 35°C = 25°C

Absolute temperature T = 25°C+273= 313K

The linear expansion formula is given by, ΔL = 𝛼LΔT,

Where, 𝛼L = 5/ ( 15 X 313)

       = 1.0649 * 10-3 K

Q 2) The main span of the London Bridge is 1500m long at its coldest. The bridge is exposed to temperatures ranging from -10ºC to 50ºC. What is its change in length between these temperatures that occurs on that bridge? Assume that the London bridge is made of steel.

Solution: 

To find the change in length, ΔL by using ΔL = αLΔT, and α, for steel is 12 × 10-6 and note that the change in temperature, ΔT, is 60ºC.

ΔL = 𝛼LΔT = (12×10-6)(1500)(60) = 1.080m

Q 3) Consider if your 90.0-L steel gasoline tank is full, so 12.0ºC is the temperature of both the tank and the gasoline. How much gasoline has to be heated so that its temperature reaches 30.0ºC?

Solution:

• to calculate the increase in the volume of the steel tank, use 

ΔV s=βsVsΔT

• To find an increase in the volume of the gasoline, use ΔVgas=βgasVgasΔT.

• Vspill= ΔVgas−ΔVs use this to determine the difference.

Vspill = (βgas – βs)VΔT

= [(950 – 35) * 10-6/ C] (90 L)(18 C)

= 1.482 L

where βgas of petrol is 950 * 10-6 and βs of steel is 35 * 10-6

THERMAL EXPANSION IN METALS

Thermal expansion is all about expansion on heating and contraction on cooling. On heating, the dimension of the objects will change. Based on the changes that occur in the body, these are the following observations:-

• If the length of the objects gets expanded, it is called linear expansion.
• On heating, if the length and breadth of the object get changed, it is called area expansion.
• If any objects expand on both sides on heating and lead to an increase in volume, it is called volume expansion.
• Some of the examples of thermal expansion in solids are molten rods, metal-framed windows, thermometers, and railway works where expansion is needed in joints of the structure. 

HEAT

• The energy present in the form of heat is called heat energy. In a hot system, there is more heat energy than is usually present in a cold system.
• Compared to humans, polar bears and icebergs have more heat energy.
• The particles like atoms and molecules present in the objects collide with each other and produce the kinetic energy of the particles. It helps to understand the concepts in better ways.

TEMPERATURE

• Whether the object is hot or cold, it can be determined with the help of temperature.
• If the energy possessed by the particles is directly proportional to the kinetic energy possessed by the particles of the substance, it is called temperature.
• It can be measured in terms of Kelvin, Fahrenheit, and celsius.
• Temperature is an independent process that does not depend on many factors such as the number, size, and quantity of the particles.