The adiabatic expansion of gases

When the gas is in such a condition that no heat can enter or leave the system during the change of volume—expansion or contraction—the temperature will generally change during the operation. This alters the magnitude of the work of expansion. Let us first find the relation between p and v when no heat enters or leaves the gas while the gas changes its volume. Boyle s relation is obscured if the gas be not kept at a constant temperature. 

L—The relation between the pressure and the volume of a gas when the volume of the gas changes adiabatically. In example (5) appended to 27, we obtained the expression, 

But ( bQ/ bT)p is the amount of heat added to the substance at a constant pressure for a small change of temperature this is none other than the specific heat at constant pressure, usually written Cp. Similarly (bQfbT)w is the specific heat at constant volume, written G . Consequently, 

This equation tells that when a certain quantity of heat is added to a substance, one part is spent in raising the temperature while the volume changes under constant pressure, and the other part is spent in raising the temperature while the pressure changes under constant volume. For an ideal gas obeying Boyle s law, 

A most important relation sometimes called Poisson s equation. 

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