Charles’ Law Formula

In 1787 French physicist Jacques Charles formulated this law. His man was holding a hydrogen balloon, while investigating he discovered that the volume of the gas in the balloon altered directly with the temperature. The relation can be stated as V/T = constant known as Charles Law. To validate this law the pressure must be constant.

The law contends that the ‘ volume of a standard gas is directly proportional to the absolute temperature at steady pressure ‘. It is an experimental gas law. Basically, it indicates how gases tend to enhance when heated.  Charles’ Law in simple words demonstrates how a gas enhances because of temperature rises. If temperature decreases, it will also lead to a decline in volume.

Charles’ Law Formula 

If the volume of an ideal gas is V and the temperature T, according to the law for steady pressure and a static proportion of the gas: 

    V = kT

●  k is constant

By reorganising the equation,

  V/T = k

Thus the correlation of volume to temperature is stable for consistent pressure and a fixed proportion of gas.

Charles’ Law Under Various Conditions

 Consider two different types of conditions. Let V1 and V2 be volumes at temperatures T1 and T2 such that the pressure of the gas is consistent. So V1 and T1 are the volume and temperature respectively at condition 1 and V2 and T2 are the volume and temperature respectively at condition 2.

By using Charles’ Law the relationship that arises between two conditions is:

V1/ T1 = k   and   V2/ T2 = k

By adding both the equations,

 V1/ T1 = V2/ T2

Thus the equation denotes that if the temperature increases consequently, the volume will also increase.

Charles’ Law Equation In Celsius Scale

We can formulate the law on the Celsius scale. As a reference point, the Celsius scale uses 0°C as a freezing point for water and 100°C for the boiling point of water. We can relate Celsius to kelvin as given below:

  T = t + 273.15

Assume the volume of gas at 0°C to be V0 and at temperature t, V will be the volume. According to Charles’ Law,

 V/ T = V0/ T0

  Replacing in the above equation,

  T = t + 273.15 and T0= t0 + 273.15 

  (V/ t) + 273.15 = (V0/ t0 ) + 273.15

 as t0 is 0°C  

  (V/ t) + 273.15 = ( 0 / t0 ) + 273.15

Reorganising the above concept,     

V = V0 ( t + 273.15 / 273.15 )

Thus, the equation is derived from Charles’ Law in the Celsius scale.

Relation To Absolute Zero

Charles’ Law seems to convey that the volume of a gas will come down to zero at a specific temperature. Gay Lussac mentioned that this law did not relate to low temperatures. At absolute zero temperature, the gas contains zero energy and hence the molecule prohibits movement. Thomson described the second law of thermodynamics in 1852, though, the ‘absolute zero’ on the kelvin temperature scale was basically defined by this second law. All the same, Charles also declared that ‘ The volume of the fixed amount of ideal gas rises or declines by 1/ 273 times the volume at 0° C for every 1° C surge or drop in temperature. Thus: 

VT = V0 + ( 1/ 273 × V0 ) × T

VT = V0 ( 1+ T/ 273 )

Here VT is the volume of gas at temperature T while V0 is the volume of gas at 0° C.

Relation To Kinetic Theory

 Kinetic theory of gases connects the apparent  properties of gases such as volume and pressure to infinitesimal properties of molecules which build up the gas, particularly the mass and speed of molecules. It is essential to have a microscopic significance of temperature to conclude Charles’ Law from kinetic theory. This can be readily taken as the temperature is proportionate to the average kinetic energy of the gas molecules (EK). From this definition, the presentation of Charles’ Law is nearly insignificant.

PV = (2/ 3) NEK

Experimental Verification of Charles’ Law

There are numerous examples of Charles’ Law to be verified, some are current though some are traditional ways. Charles’ Law refers to volume to the temperature at a steady pressure.

The apparatus consists of a conical flask and a beaker. The open flask is immersed in a water bath. When heat is provided to the beaker by the burner, it also warms the air in the flask. Condition-1. As a result, the air expands inside the flask. 

Later on, the flask is dipped in a water bath to lower the temperature, which is condition-2. Now to proceed in verification the temperature and volume for both the conditions must be known. This law is just appropriate for ideal gases. At elevated temperature and low pressure, Charles’ Law holds good for real gases. In nature at high pressures, the relationship between temperature and quantity is not linear.

Some Examples of Charles’ Law In Daily Life.

 ●      Helium balloon

●      Bakery

●      Spray bottle

●      Ping pong ball

●      Basketball

●      Tyre

●      Pool float

●      Automotive engines

●      Turkey timer

Conclusion

Charles’ Law is an experimental law of gas that depicts how gases manage to expand when heated. It expresses that if pressure is kept constant then there is a direct relationship between temperature and volume in kelvin.