Question

What does \[{P_1}{V_1}{T_1}\] and \[{P_2}{V_2}{T_2}\] mean?

Answer 1

Hint: We all have studied different laws for a gaseous system. Boyle’s law is one of them. This gas law states that pressure exerted by the gas is inversely proportional to the volume occupied at constant temperature.

Complete answer: Boyle’s law is a gas law that states that the pressure exerted by a gas of a given mass is inversely proportional to the volume occupied by the gas at a given temperature.
We can say this in other words that pressure and volume of a gas are inversely proportional to each other when the temperature and mass of the given gas is kept constant.
The mathematical relationship between volume and pressure of a gas at constant mass and temperature is as follows:
\[P \propto \dfrac{1}{V}\]
\[P = k\dfrac{1}{V}\]
Where k is a proportionality constant.
\[PV = k\]
According to Boyle's law, if any change occurred in volume of gas, then it will result in the change of pressure of gas at a constant temperature and mass of gas.
In other words, the product of initial pressure and initial volume of a gas is equal to the product of its final pressure and volume at constant temperature and mass of gas. This can be mathematically expressed as:
\[{P_1}{V_1} = {P_2}{V_2}\]
Where,
 \[{P_1}\,\] and \[{V_1}\] are the initial pressure and volume of the gas.
\[{P_2}\] and \[{V_2}\] are the final pressure and volume of the gas.
This equation is used to predict the increase in pressure exerted by a gas when the volume of the gas is changed.
In the given question, \[{P_1}{V_1}{T_1}\] and \[{P_2}{V_2}{T_2}\] represent the initial and final pressure, volume and temperature of the gases.

Note:
Some real life examples of Boyle’s law that when a filled balloon is squeezed which means pressure is increased and hence, the volume of the air inside the balloon decreases. Also, deep-sea fish die after reaching the surface of the water due to expansion of dissolved gasses in their blood.