Charless Law Relationship Between Temperature Volume

We have studied that the hot air tends to rise, which is the reason the hot-air balloons ascend upwards in the atmosphere. It is also the reason why the warm air tends to get collected near the ceilings and the cold air gets collected on the ground. Due to this behaviour, the heating registers are to be placed only near the floors and the vents in the air-conditioners are placed near the ceilings. The primary reason behind such behaviour is that the gases tend to expand whenever they get heated. Since the same amount of the substance tends to occupy the higher volume, hot air is lesser dense than the cooler air. The substances having a lower density, in this case, it is the hot air, tends to rise through that substance having a higher density, which is the cooler air.

The initial experiments for quantifying the relationship between volume and temperature os a gas were performed in the year 1783 by a French chemist and an avid balloonist, named Jacques Alexandre César Charles. His initial experiments determined that the plot of the volume of a given gas against its temperature, in degrees Celsius, at a constant pressure gives a straight line. Let us learn about the Charles Law graph, the pressure vs temperature graph, and the pressure vs volume graph.

Charles Law - Temperature and Volume Relationship

According to Charles Law, the volume of a gas having a fixed mass tends to decrease when cooled and increases when the temperature is increased. For a degree ruse in the temperature, the volume of the gas tends to get increased by 1/273 of its actual volume at 0˚C.

Consider the volume of the given gas at 0˚C and t˚C be V0 and Vt respectively.

Then,

Vt = V0 + \[\frac{t}{273.15}\]V0 …. (i) 

Vt = V0\[(1 + \frac{t}{273.15})\] …. (ii) 

Vt = V0\[(\frac{273.15 + t}{273.15})\] …. (iii) 

We can assign a new scale for the temperature in which the temperature in Celsius can be written as t = T -273.15 and 0˚C can be written as T0 = 273.15. This newer scale of the temperature, T is referred to as the Kelvin temperature scale or the Absolute temperature scale. We need to know that a degree sign is not to be written when we write the temperature in Kelvin scale. This temperature scale is also referred to as the thermodynamic scale of the temperature and is generally used in all scientific purposes. Hence, when we write the temperature in the Kelvin scale we need to add 273 to the given temperature in the Celsius scale.

Let us assume that Tt = 273.15 + t

Therefore,

T0 = 273.15

Then, we can write equation (iii) as

Vt = V0\[\frac{T_t}{T_0}\]

Or, \[\frac{V_t}{V_0}\] = \[\frac{T_t}{T_0}\]

Or, \[\frac{V_1}{T_1}\] = \[\frac{V_2}{T_2}\]

Here, \[\frac{V}{T}\] = k2, which is constant

Therefore, V = k2T

The value of the constant k2 is proportional to the amount of the gas, its pressure and its volume V.

Graphical Representation of the Relation Between Volume and Temperature

When the pressure is fixed and the volume is varied, the relationship between the volume and temperature shows as a straight line on the graph. When the volume is zero, all these lines tend to intersect at the point on the temperature axis which is at -273.15˚C. Each of the line present in the temperature vs volume graph is referred to as an isobar when the pressure is kept constant. The hypothetical temperature at -273.15˚C at which the gas tends to have zero volume is known as absolute zero.

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