# When the volume _______ at constant ________ the density increases?

##### 1 Answer

Here is an alternative answer, which emphasizes that despite the "Fill-in-the-blank" nature of the question, there are two answers.

By definition, **compression** will involve *decreasing* the **volume**, hence moving gas particles *closer* together.

**PRESSURE DEPENDENCE**

Since pressure is proportional to the density of the gas distribution, and since density is defined as

#rho = m/V# ,where:

#m# is the mass in, say, grams.#V# is the volume, in, say, liters.then since the volume decreased, the density increased.

Alternatively, using the ideal gas law:

#PV = nRT# where

#P# is pressure,#V# is volume,#n# is the#"mol"# s of gas (a measurable quantity),#R# is the universal gas constant (such as#"8.314472 J/mol"cdot"K"# ), and#T# is the temperature in#"K"# (#""^@ "C" + 273.15 = "K"# ).

When *maintain* the equality, if **the pressure must have increased**.

It does *not*, however, imply that for a **real** gas, a doubling of volume automatically implies a halving of pressure.

(That is why you will assume or have already assumed constant temperature on some ideal gas problems involving pressure and volume).

**TEMPERATURE DEPENDENCE**

Since some of the compression *decreases* the distance between each gas, it increases the likelihood of *potential collisions*, but decreases the "wiggle room" between gas particles. Each collision would *transfer* some **kinetic energy** between gas particles, but **not a lot of it can be used** since the particles can't move around as much.

So, the kinetic energy is constantly *redistributed* into the **potential energy** of the still gas particles (as per *conservation of energy*, energy is neither created nor destroyed, but redistributed).

(That is,

Since more gas particles have greater potential energy, it follows that the **average kinetic energy** has *decreased*, and consequently, since that is the *definition* of the temperature, **the temperature has decreased as well**.

This can be mathematically proven via the ideal gas law as before:

#PV = nRT#

When