Section B
16.
Answer the following Questions. [Each carries 2 marks]
Explain Boyle's law and derive its equation and plot isothermal graph,
Answers
Explanation:
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
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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
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.