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1800-102-2727Each of us has encountered a syringe when visiting a doctor. It is a medical tool used for fluid injection or withdrawal. It is made up of a sliding plunger attached to a hollow barrel. A syringe functions similarly to a reciprocating pump. The fluid will inject when the plunger is pressed, and it will withdraw when the plunger is pulled.
Do you think, what is happening? The amount of fluid in the barrel decreases as the plunger is pushed. Due to a momentary increase in pressure brought on by the volume reduction, the fluid is then pushed into the patient's body. Similar to this, pulling the plunger expands the fluid's volume. The fluid's pressure briefly drops as a result, and external fluid is extracted. This can be explained by the boyle's law. Let's learn what Boyle's law is !
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According to the law, as long as the temperature of a closed system doesn't vary, the absolute pressure and volume of a given amount of confined gas are inversely related. At constant mass and temperature, the volume-pressure relationship for a gas can be mathematically described as follows.
$P\propto \frac{1}{V}$
Where, P is the pressure the gas is exerting, and V is the volume it is occupying. By including the constant k, this proportionality can be transformed into an equation as,
$P=\frac{k}{V}$
PV=k
Hence Boyle's law states that if a gas's pressure doubles while its temperature remains constant, its volume will also be reduced by half. The cause is the intermolecular force that exists between the molecules of the gaseous substance. A gaseous substance occupies more area in a container when it is free due to the dispersed nature of the molecules.
The graph below shows the pressure v/s volume curve for a set mass of gas kept at a constant temperature.
If we draw a graph between the pressure and the reciprocal of the volume, then it will be straight line as shown in figure below,
According to Boyle's law, a gas's pressure will change whenever its volume changes, given its quantity and temperature remain constant. In other words, the product of a gas's initial pressure to its initial volume is equal to the product of gas's final pressure to that final volume (at constant temperature and number of moles). If P_{1}, V_{1} is the initial pressure and volume of the of the system and P_{2}, V_{2} is the final pressure and volume of the system, then this law has the following mathematical formulation:
${P}_{1}{V}_{1}={P}_{2}{V}_{2}$
Or $\frac{{P}_{1}}{{P}_{2}}=\frac{{V}_{2}}{{V}_{1}}$
When a gas's container's volume is reduced, this equation can be used to determine how much pressure will increase on the container's walls (when its quantity and absolute temperature remain unchanged).
Boyle's law describes how a gas's pressure and volume are related. Robert Boyle made the first discovery in the seventeenth century. He discovered that, given a fixed quantity of gas, the pressure of a gas is inversely proportional to its volume at constant temperature. Following are some examples or applications from real-world situations.
Q1. At room temperature, hydrogen is inflated into a balloon. If the pressure goes over 1.3 bar, it will burst. What volume may the balloon be expanded to if the gas has a 3.45 L volume at 1 bar pressure?
Answer. Given ${P}_{1}=1bar$ and V_{1}=3.45 L
And P_{2}=1.3 bar
According to the Boyle’s law,
${P}_{1}{V}_{1}={P}_{2}{V}_{2}$
$1\times 3.45=1.3\times {V}_{2}$
V_{2}=2.6538 L
The volume of the balloon is 2.6538 L.
Q2. A specific amount of gas is present in a vessel with a 150 mL capacity at 1.5 bar pressure and 28 °C. The gas is then transferred to a 200 mL vessel at 28 °C. What pressure would it have?
Answer. Given ${P}_{1}=1bar$r and V_{1}=150 mL
And V_{2}=200 ml
According to the Boyles’ law,
${P}_{1}{V}_{1}={P}_{2}{V}_{2}$
$1.5\times 150={P}_{2}\times 200$
P_{2}=1.125 bar
The pressure of the gas is 1.125 bar
Q3. A gas takes up 20 liters at 37 mm Hg of pressure. When the pressure is raised to 50.0 mm Hg, what is the volume?
A. Given P_{1}=37 mm Hg and V_{1}=20 liters
And P_{2}=50.0 mm Hg
According to the Boyles’ law,
${P}_{1}{V}_{1}={P}_{2}{V}_{2}$
$37\times 20=50\times {V}_{2}$
V_{2}=14.8 liters
The volume of the gas is 14.8 liters.
Q4. What pressure does an atmospheric gas need to be compressed to in order to fit a 400.0 cubic feet of gas into a 3 cubic foot tank?
Answer. Given P_{1}=1 atm and V_{1}=400.0 cubic feet
And V_{2}=3 cubic foot
According to the Boyles’ law,
${P}_{1}{V}_{1}={P}_{2}{V}_{2}$
$1\times 400={P}_{2}\times 3$
P_{2}=133.33 atm
Hence the pressure needed is 133.33 atm.
Q1.Under what circumstances Boyle's law is relevant?
Answer: In an isothermal process where the temperature stays constant, Boyle's law is applicable.
Q2. Is Boyle's law applicable to liquids?
Answer: Liquids cannot be compressed, like gasses, because their particles are already relatively closely spaced. So Boyle's law is not applicable to liquids.
Q3. Why does Boyle's law not apply in high pressure situations?
Answer: Boyle's law only holds true at low pressure because at high pressure, gases do not behave like ideal gasses.
Q4. How does Boyle's law operate?
Answer: According to Boyle's law, the relationship between a gas's pressure and volume is inverse at a given temperature. I.e. when the temperature remains the same, pressure rises as volume decreases and vice versa.