Boyle’s law is a gas law which states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. Boyle’s law was put forward by the Anglo-Irish chemist Robert Boyle in the year 1662.
For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed mathematically as follows.
P ∝ (1/V)
Where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant, k.
P = k*(1/V) ⇒ PV = k
The pressure v/s volume curve for a fixed amount of gas kept at constant temperature is illustrated below.
It can be observed that a straight line is obtained when the pressure exerted by the gas (P) is taken on the Y-axis and the inverse of the volume occupied by the gas (1/V) is taken on the X-axis.
Formula and Derivation
As per Boyle’s law, any change in the volume occupied by a gas (at constant quantity and temperature) will result in a change in the pressure exerted by it. In other words, the product of the initial pressure and the initial volume of a gas is equal to the product of its final pressure and final volume (at constant temperature and number of moles). This law can be expressed mathematically as follows:
P1V1 = P2V2
Where,
- P1 is the initial pressure exerted by the gas
- V1 is the initial volume occupied by the gas
- P2 is the final pressure exerted by the gas
- V2 is the final volume occupied by the gas
This expression can be obtained from the pressure-volume relationship suggested by Boyle’s law. For a fixed amount of gas kept at a constant temperature, PV = k. Therefore,
P1V1 = k (initial pressure * initial volume)
P2V2 = k (final pressure * final volume)
∴ P1V1 = P2V2
This equation can be used to predict the increase in the pressure exerted by a gas on the walls of its container when the volume of its container is decreased (and its quantity and absolute temperature remain unchanged).
Examples of Boyle’s Law
When a filled balloon is squeezed, the volume occupied by the air inside the balloon decreases. This is accompanied by an increase in the pressure exerted by the air on the balloon, as a consequence of Boyle’s law. As the balloon is squeezed further, the increasing pressure eventually pops it. An illustration describing the increase in pressure that accompanies a decrease in the volume of a gas is provided below.
If a scuba diver rapidly ascends from a deep zone towards the surface of the water, the decrease in the pressure can cause the gas molecules in his/her body to expand. These gas bubbles can go on to cause damage to the diver’s organs and can also result in death. This expansion of the gas caused by the ascension of the scuba diver is another example of Boyle’s law. Another similar example can be observed in the deep-sea fish that die after reaching the surface of the water (due to the expansion of dissolved gasses in their blood).
Charles law also sometimes referred to as the law of volumes gives a detailed account of how gas expands when the temperature is increased. Conversely, when there is a decrease in temperature it will lead to a decrease in volume.
When we compare a substance under two different conditions, from the above statement we can write this in the following manner:
V2/V1=T2/T1
OR
V1T2=V2T1
This above equation depicts that as absolute temperature increases, the volume of the gas also goes up in proportion.
In other words, Charle’s law is a special case of the ideal gas law. The law is applicable to the ideal gases that are held at constant pressure but the temperature and volume keep changing.
Charles Law Everyday Examples
Here are some of the examples by which you can understand Charle’s law very easily.
In winters as the temperature decreases, when u take a basketball outside in the ground the ball shrinks. This is the only reason why to check the pressure in the car tier’s when to go outside in the cold days. This is also the case with any inflated object and explains why it’s a good idea to check the pressure in your car tires when the temperature drops.
If you overfill a tube that is placed on a pool on a hot day, it can swell up in the sun and burst. Similarly, as the turkey cooks, the gas inside the thermometer expands until it can “pop” the plunger. Pop-up turkey thermometers work based on Charles’ law. Another common application can be seen in the working of a car engine.
Charles Law Formula
Charle’s Law formula is written as,
VI /TI=VF /TF
Where VI=Initial volume
VF=Final volume
TI=Intial absolute temperature
TF=Final absolute temperature
Here we should remember that the temperatures are absolute temperatures that are measured in Kelvin, not in ⁰F or ⁰C.
Derivation of Charles Law
As we are aware of the fact that, at constant pressure, the volume of the fixed amount of the dry gas is directly proportional to absolute temperature according to Charle’s law. We can represent the states in the following manner.
V∝T
Since V and T are varying directly, we can equate them by making use of the constant k.
V/T=constant =k
In this, the value of k depends on the pressure of the gas, the amount of the gas and also the unit of the volume.
V*T=k——-(1)
Let us consider V1 AND T1 to be the initial volume and the temperature respectively of an ideal gas.
Then we can write equation (1) as
V1/T1=k——-(2)
After it lets change the temperature of the gas to T2. Alternatively, its volume changes to V2 then we can write
V2/T2=k——–(3)
Equating the above equations that is equation 2 and 3, we get
V1/T1=V2/T2
OR
V1T2=V2T1
You are unaware of the fact that, on heating up a fixed amount of gas, that is, by increasing the temperature the volume also increases. Similarly lowering the temperature, the volume of the gas decreases. And at 0-degree centigrade, the volume of the also increases by 1/273 of its original volume for a unit degree increases in temperature.
It is important to know, as already discussed above that the unit of temperature must be in Kelvin not in Celcius or Fahrenheit for solving the problems related to Charle’s law. The temperature in Kelvin is also known as the absolute temperature scale. For converting the temperature in Celcius to Kelvin, you add 273 to the temperature in the Celsius scale.
According to Charles’ Law which states that the volume (V) of the gas is directly proportional to its temperature (T) which must be in Kelvin.
When the temperature changes one unit of the Kelvin scale it equals to a change in one Celsius degree. Remember always that 0 on the Kelvin scale means -273 or “Absolute Zero”.
The Density of the gas is inversely proportional to the temperature in the Kelvin when it is at a constant mass and pressure.
Graphical Representation Of Charles Law
ISOBAR- Graph between V and T at constant pressure is known as isobar or bioplastics and it always gives a straight line. A plot of V versus T (°C) at constant pressure is a straight line at – 273.15°C. -273.15-degree Celcius is the lowest possible temperature.
Avogadro’s Law – N α V at Constant Pressure:
When there is a greater number of particles it increases the collisions and the pressure. If the pressure is to remain constant, the number of collisions can be reduced only by increasing the volume.
At constant pressure, the volume is proportional to the amount of gas.