Thermal Expansion Concept Page - 3

Example

Disadvantages of thermal expansion of liquids

The disadvantages of thermal expansion of liquids are as follows:
1. We should not use pure water in the radiator as water has a far higher coefficient of volume expansion than a typical engine coolant. This can be particularly hazardous in cold weather, because frozen water in a radiator could expand enough to crack the engine block.
2. In cold weather, water in the pipes freezes and expands which leads to bursting of pipes.

Example

Thermal Expansion in liquid

Liquids expand when its atoms vibrate faster about their fixed points, but because the bonds between separate molecules are usually less tight they expand more than solids. This is the principle behind liquid-in-glass thermometers. An increase in temperature results in the expansion of the liquid which means it rises up the glass.

Example

Thermal Expansion in gases

When gases are heated pressure and volume change, gases have large thermal expansion because of large intermolecular distance between the molecules of the gas .
There are two types of expansions of gases
1) Volume expansion of gas
2) Pressure expansion of gas 
 Example of thermal expansion in gases can be observed in hot air baloons,  when the gas is heated the baloon inflates.

Example

coefficient of volume expansion of liquids

Coefficients of cubical or volumetric thermal expansion of some common liquids:

Material	Volumetric coefficient of expansion (10−4 oC−1${10}^{-4}{{}^{o}C}^{-1}$)
Mercury	1.8
Engine Oil	7
Petroleum	10
Chloroform	12.7
Benzene	12.5

Formula

Average coefficient of volume expansion

γ¯¯¯=1VΔVΔT$\overline{\gamma }={\displaystyle \frac{1}{V}}{\displaystyle \frac{\mathrm{\Delta }V}{\mathrm{\Delta }T}}$
where γ¯¯¯$\overline{\gamma }$ is the average coefficient of volume expansion

Diagram

Variation of coefficient of volume expansion with t

Example

Real and apparent expansion of liquid

A liquid is heated in a container. Heat flows through the container to the liquid. This means that the container expands first, due to which the level of the liquid falls. When the liquid gets heated, it expands more and beyond its original level. We cannot observe the intermediate state. We can only observe the initial and the final levels. This observed expansion of the liquid is known as the apparent expansion of the liquid and is less than its actual expansion. 

Formula

Relation between Real and apparent expansion of liquid

Real expansion of the liquid = Apparent expansion of the liquid + Volume expansion of the container

Definition

Coefficient of volume expansion for ideal gas at constant pressure

Show that the volume thermal expansion coefficient for an ideal gas at constant pressure is 1T${\displaystyle \frac{1}{T}}$.We know by ideal gas equation that PV=nRT$PV=nRT$
Thus, at constant pressure, V=nRPT$V={\displaystyle \frac{nR}{P}}T$
ΔV=nRPΔT$\mathrm{\Delta }V={\displaystyle \frac{nR}{P}}\mathrm{\Delta }T$
Dividing the two equations,we get ΔVV=ΔTT${\displaystyle \frac{\mathrm{\Delta }V}{V}}={\displaystyle \frac{\mathrm{\Delta }T}{T}}$
Hence, ΔV=VΔTT$\mathrm{\Delta }V=V{\displaystyle \frac{\mathrm{\Delta }T}{T}}$ and γ=1T$\gamma ={\displaystyle \frac{1}{T}}$.

Example

Examples of expansion of liquid and gases

Explain what happen when liquids are heated?
When a liquid is heated, its molecules gain kinetic energy and vibrate more vigorously.  As the vibration become larger, the molecules are pushed further apart and the liquid expands slightly in all directions.

Explain why when heating a liquid, its level initially decreases and then it increases to become more larger than the original level?
The liquid level drops due to the expansion of its container which initially absorbed all the heat.  After a while, the heat reaches the liquid it compensates for the expansion of the container and rises much more than the original level.

Explain the effect of temperature on gas volume when pressure is constant?
When pressure is constant, the volume of a gas is directly proportional to the Kelvin temperature (Charlie's Law).When the temperature of a gas is increased, the molecules move faster and the collisions become more violent thus they spread away from each other causing the volume to increase. 

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