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# Boyle’s Law- Statement, Equation, Representation, Applications, Practice Problems & FAQs

To understand Boyle’s law, let's look at the following setup. What [1] do you think would happen if we press the plunger of the syringe? Yes, you got it correct![2] The volume will decrease but at the same time, the pressure of the air inside the syringe will increase[3] . In the year 1662, Robert Boyle showed the relationship between pressure and volume of gas through different experimental observations and named it Boyle’s law which helps to explain different observations in everyday life.

Table of content

• Statement of Boyle’s law
• Equation of Boyle’s law
• Graphical representation of Boyle’s law
• Applications of Boyle’s law
• Practice problems

## Statement of Boyle’s law

According to Boyle’s law “At constant temperature and for a fixed amount of gas, the pressure of the gas varies inversely with the volume of the gas”.

## Equation of Boyle’s law

Mathematically it can be represented as;

Constant

Where represents pressure exerted by the gas, is the volume occupied by the gas and represents the constant of proportionality.

Note: The above relation of pressure and volume is shown considering the temperature and amount of gas to be constant.

Mathematical representation of Boyle’s law under two different pressure and volume conditions:

Using Boyle’s law for both Case and Case, we get;

From equation and , we get,

Constant

Where represent pressure exerted by the gas and volume occupied by the gas in Case respectively and represent the pressure exerted by the gas and volume occupied by the gas in Case respectively.

## Graphical representation of Boyle’s law

The curve for a fixed amount of gas and at a constant temperature is represented as;

According to the equation;

Pressure exerted by the gas is inversely proportional to the volume occupied by the gas, so if pressureis taken on the -axis and volume on the -axis, the nature of the curve would be rectangular hyperbola and you can see from the graph that pressure is increasing when the volume is decreased.

## Applications of Boyle’s law

• Filling of natural gas in containers
• Working of a cylinder-piston arrangement
• Wearing spacesuit in space
• Ascending gradually during scuba diving

## Practice problems

Q1. A cylinder with flexible walls containing nitrogen at a pressure of is allowed to expand at constant temperature such that the final pressure of the nitrogen becomesThe final volume of the cylinder is: (Assuming nitrogen present in the flask behaves ideally)

Solution:

According to the given data,

Initial volume of the cylinder

Initial pressure of nitrogen gas in the cylinder

Final pressure of nitrogen gas in the cylinder

Let the final volume of the cylinder be

Using Boyle’s law we get,

Putting the values in the above expression we get,

Q2. An ideal gas undergoes compression at a constant temperature, which reduces its volume by. The final pressure and the volume of a gas are and respectively. Calculate the original pressure of the gas in .

Solution: Let the original pressure be .

Initial volume of the gas Final volume of the gas + Reduction in volume

Final pressure exerted by the gas

Using Boyle’s Law and putting the values we get,

Q3. Calculate the percentage change in volume of an ideal gas if it is compressed at from to

Solution: Let the initial and final volume of an ideal gas be and respectively.

Initial pressure

Final pressure

Using Boyle’s Law and putting the values we get,

% Change in volume =

100}

Putting value of from equation

100}

Note: sign here signifies a decrease in volume of an ideal gas.

Q4. Slope of the plot between and at constant temperature is_______.

Solution:

As shown in the graph above plot is parallel to the axis and therefore,

Slope

Q1. How does Boyle's law have practical application in scuba diving?

Answer: We are aware of the fact that according to Boyle's law, pressure and volume are inversely related to each other. So, if a diver takes a lung full of air underwater, that air will expand his lungs as he rises to the surface because the pressure is higher underwater and at the surface, pressure is reduced. If he ascends too rapidly or holds his breath the expanding air can rupture his lungs.

Q2. How density of gas and pressure can be related considering the gas obeying Boyle’s law?

Answer: According to Boyle’s law we know that pressure and volume are inversely related considering temperature and amount of gas to be constant.

, since the amount of gas is assumed to be constant.

Therefore, .

According to Boyle’s law,

Pressure of the gas

So, considering , it can be said as;

Density of the gas is directly proportional to the pressure of the gas.

Q3. Why do inflated balloons burst when it is compressed?

Answer: When the inflated balloon is compressed its volume decreases. We know, according to Boyle’s law, pressure is inversely proportional to the volume of the gas. Therefore, on decreasing the volume of the inflated balloon pressure inside the balloon increases and it burst.

Q4. Why are gases highly pressurized while storing them in a small container?

Answer: Gases are generally pressurized when stored in a small container. We know, according to Boyle’s law, pressure is inversely proportional to the volume of the gas. Therefore, pressurizing the gas decreases the volume occupied by the gas and a larger volume can be stored in the small containers.

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