Question

When we inflate cycle tubes, the volume of the tube as well as the pressure of air inside the tube increases.
A.It is an exceptional case of Boyle’s law
B.It happens because air is not ideal gas
C.It happens because mass of air is not constant
D.It happens because external force is applied in inflating the tube.

Answer 1

Hint: When we inflate the tube then we inject air into the tube then volume and pressure of the tube increases because mass of air is not constant. And for Boyle’s number of moles should remain constant.

Complete step by step solution:
First of all we should know what is ideal gas equation:
Ideal gas equation: It is defined as the relation between temperature, pressure, number of moles of gas and volume of gas. The equation which relates all these parameters are as: ${\text{PV = nRT}}$ where $P$ is the pressure, $V$ is the volume, $n$ is number of moles, $R$ is universal gas constant and $T$ is the temperature. Standard temperature and pressure (STP) is ${0^ \circ }C$and $1atm$.The volume of $1{\text{ mole}}$ of an ideal gas at (STP) is $22.41L$, which is known as standard molar volume.
Derivation of ideal gas law:
Charle’s law states that at constant pressure and constant number of moles of a gas volume is directly proportional to the temperature i.e.$V\propto T$
Boyle’s law states that at constant at temperature and constant number of moles pressure is inversely proportional to the volume i.e. $P\propto\dfrac{1}{V}$
Avogadro’s law states that at constant temperature and pressure volume is directly proportional to the number of moles i.e. $V \propto n$
Combining all these laws we get ideal gas law which is $PV = nRT$.
Now, when we inflate the tubes then the volume as well as pressure of the tube increases because mass of the air is not constant. As mass is not constant it means the number of moles is not constant. And there is no violation of Boyle's law here because for Boyle's law there is a condition that the number of moles should remain constant so here we cannot apply Boyle's law as the number of moles are not constant.

Hence, option C i.e. it happens because mass of air is not constant is correct.

Note: We can apply laws only when the conditions are satisfied. As in this question as moles are not constant so we cannot apply Boyle's law. And also we cannot apply Charles law to calculate the relation between volume and temperature in this condition as conditions are not followed i.e. number of moles are not constant.