Fluid Mechanics – Gas Laws

Gas laws are first equation of state that shows relationship temperatures and pressures of gases. Gas Laws explain about changes in behavior of gas when certain conditions are applied. Gas laws deal with how gases behave with respect to volume, pressure, temperature and amount. Following are some of important gas laws.

  • Boyle’s Law
  • Charles’ Law
  • Gay-Lussac’s Law or Amontons’ Law
  • Avogadro’s Law
  • Universal Gas Law Formula

Boyle’s Law

Boyle’s Law states that, when temperature, pressure and volume of gas are constant are inversely proportional. Boyle’s law show relationship between pressure and volume of gas if temperature is constant. It gives us important information about behavior of gases. Also read Viscosity in Fluid Mechanics

In this case, we find pressure and volume of gas are inversely proportional to one another. This law applies only to ideal gases which allow only pressure and volume to change. In other words, product of pressure and volume is constant for fixed mass of ideal gas at fixed temperature.

Boyles’ Law can also be used to compare two gases using this formula. Boyle’s Law Formula can be expressed as

P_{1}V_{1}=P_{2}V_{2}

Where  is Initial Pressure,  is Final Pressure. And is Initial Volume and  is final volume. In this equation, Pressure and volume have direct relationship, so if volume goes up then pressure goes down and if pressure goes up the volume goes down and vice-versa.

Charles’ law

Charles law is second of gas laws and also known as law of volumes. This law tells you about relationship between volume and temperature of gas. It states that volume of gas is directly proportional to its temperature. This law is valid as long as amount of gas and pressure is constant. So temperature must be an absolute temperature.

It describes how gases expand when heated. When two dimensions are in direct proportion then any change made in one of them affects other through direct variation. As volume goes up, temperature also goes up and vice-versa. You can also see Bernoulli’s principle from Equation in Fluid Mechanics 

Charles’ Law equation is follows-

According to Charles’ Law, P is constant pressure and V volume is directly proportional to temperature T.

V\alpha T or V = kT, where k is constant.

Charles’ Law is also written as:  =\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}

Where V1 is initial volume and T1 is Initial temperature in Kelvin or absolute scale. Whereas V2 is final Volume of gas and T2 is Final Temperature in Kelvin or absolute scale. Both the temperatures are in units of Kelvin. This equation can be used for initial or final value of volume or temperature under given conditions that pressure and number of gas mole stays the same.

Gay-Lussac’s Law

Gay-Lussac’s Law states that constant volume pressure is directly proportional to Kelvin temperature for given amount of gas. This relationship between temperature and pressure is known as Gay-Lussac’s Law As pressure goes up, temperature also goes up, vice-versa. Also, initial and final volumes and temperatures under contact pressure.

\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}

Where P1 is volume and P2 is final volume. And also T1 is temperature and T2 is final temperature. Gay-Lussac’s Law is applicable only to gases. On other hand, volume of gas is directly proportional to Kelvin temperature if volume is kept constant.

In addition to this, units for temperature must be Kevin or equation will not work. Also, note that units for pressure as long as they are same throughout equation. This is because Kelvin scale is an absolute scale so it does not go negative. Finally, this equation only works for an ideal gas.

Avogadro’s Law

Avogadro’s Law is one of gas laws. Avogadro’s Law deals with relationship between volume of gas and amount of moles of gas present. It also states that, under same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules.

According to Avogadro’s Law, volume of will be directly proportional to amount of moles of gas at constant temperature and constant pressure.

You can express this equation as follows:

\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}

Where V1 is initial volume of gas and n1 is initial quantity of gas in moles. And V2 is final volume of gas and n2 is final volume of gas in moles. We can also say that if amount of moles of gas will increased then volume of gas will also increased. At given temperature and pressure, equal volume of gas will have equal number of moles of gas.

Universal Gas Law Formula

When gas combine law check the behavior of constant amount of gas when pressure and temperature is allowed to change. In other words, product of pressure multiplied by volume and divided by temperature is constant.

However, law is used to compare before or after conditions. Now we can combine everything we have into one proportion. Then according to Combined Gas law is derived from three gas laws Boyles law, Charles law and Gay-Lussacs law. This combined gas law equation is written as follows:

\frac{P_{1}V_{1}}{n_{1}}=\frac{P_{2}V_{2}}{n_{2}}

Let P1, V1 and T1 is initial pressure, volume and temperature at Kelvin scale. Similarly, P2, V2 and T2 will be final pressure, volume and temperature in Kelvin scale of given mass of gas. This is final form of combined gas law equation.

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