Can we liquefy the Earth’s atmosphere? And do you know the behavior of gases under very low temperature? Are there any laws that govern the behavior of gases? Here we shall learn about the various interesting properties of gases. Read out more in this section.

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## Behavior of Gases

There are 5 main states of matter: solid, liquid, gas, plasma and the Bose-Einstein condensate. Out of these gases are a special state. Their properties are easy to study. We see that gases follow certain laws known as the gas laws. These laws tell us about the behavior of gases. By that, we mean the values and relations of temperature, pressure and volume etc. Let’s see what these laws are.

**Browse more Topics under Kinetic Theory**

- Specific Heat Capacity and Mean Free Path
- Law of Equipartition of Energy
- Kinetic Theory of an Ideal Gas

**Gas Laws**

In the periodic table of elements, we have the group of inert gases or permanent gases which are very unreactive. Their properties are very close to an ideal gas and hence their behavior resembles that of an ideal gas. On the basis of certain experiments using inert gases, the following laws governing the behavior of gases were established:

### Boyle’s Law

Suppose you have some Helium in a gas container at a low pressure and temperature. At a constant temperature, if you increase the volume of the container, the pressure of the gas will decrease. This is given by the Boyle’s law.

This law states that at a constant temperature, the volume (V) of a given mass of gas is inversely proportional to its pressure (p). At constant temperature, Boyle’s law can be stated as

V \( \propto \) 1/P or VP = constant ….(1)

The constant is a proportionality constant. Its values depend on the mass, temperature and nature of the gas. If P_{1} and V_{1} are the initial values of pressure and volume of any gas and P_{2} and V_{2} are another set of values, then we can say that

P_{₁}V_{₁} = constant …(2) and P_{2}V_{2} = constant …(3)

Since the mass, temperature and nature of a gas are same throughout, we say equation (2) and (3) represent the same quantity. Thus we have:

P_{₁}V_{₁} = P_{2}V_{2}

### Charles’ Law

A similar relation is found between Volume and Temperature of an ideal gas. We call it the Charle’s Law. This law states that at constant pressure, the volume (V) of a given mass of gas is directly proportional to its absolute temperature (T).

If V is the volume and T is the temperature of a gas at some constant pressure, then V \( \propto \) T or V/T = constant. Following the same method as above, we can write:

V₁/T₁ = V₂/T₂

### Gay Lussacs’ or Regnault’s Law

This law states that at constant volume (V), the pressure (P) of a given mass of a gas is directly proportional to its absolute temperature (T). We can write: P \( \propto \) T or P/T = constant. Also, we can write:

P₁/T₁ = P₂/T₂

### Kinetic Theory of Gases

### Avogadro’s Law

This law stat

es that equal volumes of different gases, under similar conditions of temperature and pressure, contain equal number molecules. This means that if you have two or more different gases, as long as they have similar conditions of temperature and pressure, equal concentrations of these gases will occupy equal portions of volume.

For example, at STP (Standard Temperature and Pressure) or NTP, where T = 273K and p = 1 atm, 22.4L of each gas has N_{A }= 6.023 x 10^^{23} molecules. In other words, one mole of any gas under STP conditions occupies 22.4L volume.

## Standard Gas Equation

Gases which obey all gas laws under all conditions of pressure and temperature are called perfect gases or the ideal gases. Inert gases kept under high temperature and very low pressure behave like ideal gases. Equation of state for a perfect gas can be written as

PV=nRT

where, p = pressure, V = volume, T = absolute temperature, R = universal gas constant = 8.31 J mol^{-1} K^{-1}, n = number of moles of a gas

### Real Gases

None of the gases that exist in nature, follow the gas laws for all values of temperature and pressure. So we see that the behavior of gases that exist or the “real gases” differs from the behavior of the ideal gases. These gases deviate from ideal gas laws because:

- Real gas molecules attract one another.
- Real gas molecules occupy infinite volume.

Hence the equations for such gases need modifications as discussed below.

#### Real Gas Equation or Van der Waal’s Gas Equation

The equation of state for a real gas can be written as:

(P + a/V²) (V-b) = RT

where, a and b are Van der Waal’s constants.

## Solved Examples For You

Q: Assertion: If the pressure of an ideal gas is doubled and volume is halved, then its internal energy will remain unchanged.

Reason: The internal energy of an ideal gas is a function of temperature only.

- Both the Reason and Assertion are correct and Reason is the correct explanation of Assertion.
- Both are correct but Reason is not the correct explanation of Assertion.
- The assertion is correct but Reason is wrong.
- The reason is correct but Assertion is wrong.

Solution: A). Let P’ = 2P and V’ = V/2. Then from the equation of the state, P’V’ = nRT, we have from substitution PV = nRT. This shows that temperature doesn’t change and as the Internal energy of an ideal gas is a function of Temperature only, the internal energy of the gas will remain same.

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