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### Change Due to Heat

• As an object's temperature rises, its dimensions will begin to increase. Different materials have different coefficients of linear expansion (α). The change in length is given by
 ∆L = L α(∆T).
• Similarly, the volume will also increase as the temperature rises. The coefficient of volume expansion is β = 3α.
 ∆V = V β(∆T).
• The above two formulas do not work for gases. They work fine for solids and liquids, but because gases already expand to fill their container, we need a different equation. And for that, we need-
• -The Mole (mol) is a measure of how many atoms/molecules/objects there are in a substance. If m is the molecular mass of the substance and M is the mass of the substance in grams, then n=[M/m] is the number of moles.
• In a mole there are NA = 6.022 ·1023   [objects/mol]. This is called Avogadro's number.
• We can model the behavior of a gas with the Ideal Gas Law:
 pV = nRT.
• p is the pressure of the gas. [Note: absolute, not gauge pressure].
• V is the volume of the gas.
• n is the number of moles of gas.
• R is the gas constant: R = 8.314 [J/(mol·K)].
• T is the temperature (in kelvin) of the gas.
• As more and more thermal energy is added to a substance, it will change phase: first from solid to liquid, then from liquid to gas. If thermal energy is removed, it will do the reverse. The specific change over temperatures vary depending on pressure.
• It takes thermal energy to change phase. The amount of heat depends on the substance and the mass of the object:
 Q = Lm,
where L is a proportionality constant that varies depending on substance and phase type. This heat is put into the substance if it is going to a higher energy phase, and removed if going to a lower energy phase.

## Change Due to Heat

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