## Thermal Properties of Matter

# Thermal Expansion

- Linear expansion (or) increase in length of rod depends on nature of material, initial length of rod and rise of temperature.
- Numerical value of coefficient of linear expansion of solid depends on nature of material, scale of temperature and is independent of physical dimensions of body
- Numerical value of coefficient of linear expansion of a solid is "αC" when temperature is measured in celsius scale and its value is "αF" when temperature is measured in Fahrenheit scale then αF = (5/9) αC
- If a hollow pipe and a solid rod of same dimensions made of same material are heated through the same rise of temperature both expand equally.
- A thin rod and thick rod made of same material have same initial lengths if they are heated to equal temperature difference both expand equally.
- A thin rod and thick rod made of same material have same initial if they are heated by equal quantities of heat thin rod expands more.
- When a solid is heated its moment of inertia increases.
- Metal tape shows correct reading only are temperature at which it is calibrated and correction Δ C = L α (t
_{2}− t_{1}) - Primetallic strip is a combination of two metal strips of different linear coefficients and of same length riveted together firmly. Radius of it = \tt \frac{d}{\left(\alpha _{2}-\alpha _{1}\right)\Delta t}
- A rod is clamped at its ends and prevented without expansion. Then thermal stress = Y αΔT.
- Pendulum clocks are made of invaar steel to avoid error in time measurement.
- Liquids have definite volume but do not have definite shape so they have only cubical expansion.
- Expansion of liquid relative to container called apparent expansion.
- Expansion of liquid independent of expansion of container is called Real expansion.
- Relation between two coefficients γR = γa + γg where γR is coefficient of real expansion γa = coefficient of apparent expansion.
- Expansion of mercury is nearly 7 times that of glass. If glass vessel is filled with 1/7 th of its volume with mercury.
- Liquids expand on heating but water at 0°C on heating contracts upto 4°C and expands beyond 4°C and is called anamalous behaviour water.
- Gases do not have fixed size and shape but they have pressure and fixed volume when heated both pressure and volume changes simultaneously.
- At absolute zero the pressure and volume of a gas both would be zero.
- According to Boyles law at constant temperature the pressure of given mass of gas is inversely proportional to the volume of gas.
- The graph between pressure and volume of a gas at constant temperature in the shape of rectangular hyperbola.
- Real gases obey all gas laws at high temperature and low pressure.
- According charlers law at constant pressure the volume of a gas is directly proportional to its absolute temperature.
- According to Gay Lussac's Law at constant volume for a given mass pressure is proportional to temperature.
- Ideal gas equation is PV = nRT when n = no of moles R = universal gas constant T = absolute temperature.

### Thermal Expansion View the Topic in this video From 42:58 To 1:00:35

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1. The coefficient of volume expansion (or volume expansivity). \tt \alpha_{v}\ as \ \alpha_{v}=\left(\frac{\Delta V}{V}\right)\frac{1}{\Delta T}

2. The coefficient of volume expansion at constant pressure can be found from the ideal gas equation:

PV = *μRT*

At constant pressure

PΔV = *μR *Δ*T*

\tt \frac{\Delta V}{V}=\frac{\Delta T}{T}

3. **Linear expansion** If a rod is having length *l*_{0} at temperature *T*, then expansion in length of rod due to rise in temperature by Δ*T* is given by Δ*l = l _{0 }*α ΔT

4. **Superficial expansion** is valid only for solids. This is given by *A _{f} *= A

_{0}(1 + β × Δ

*T*)

5. **Cubical expansion** Volume after expansion, *V* = *V*_{0}(1 + γΔT), where γ is the **coefficient of cubical expansion**.