Question

A sample of air occupies $10{\text{ L}}$ at ${127^ \circ }{\text{C}}$ and $1{\text{ atm}}$ pressure. What volume of air will be expelled when it is cooled to $- {23^ \circ }{\text{C}}$ at the same pressure?

Answer 1

The pressure is kept constant and the volume and temperature are varied. Thus, Charles’s law can be applied in this case.

Complete step by step answer:
We know that the pressure is the same i.e. $1{\text{ atm}}$.
The temperature is varied from ${127^ \circ }{\text{ C}}$ to $- {23^ \circ }{\text{ C}}$. And we have to calculate the change in volume.
Charles's law states that when the pressure of the gas is constant, the volume of the gas and the temperature of the gas are in direct proportion to each other.
The equation for Charles’s law is as follows:
$\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$
Thus,
${V_2} = \dfrac{{{V_1}}}{{{T_1}}} \times {T_2}$
Substitute $10{\text{ L}}$ for ${V_1}$, ${127^ \circ }{\text{C}} + 273 = 400{\text{ K}}$ for ${T_1}$, $- {23^ \circ }{\text{C}} + 273 = 250{\text{ K}}$ for ${T_2}$. Thus,
${V_2} = \dfrac{{10{\text{ L}}}}{{400{\text{ K}}}} \times 250{\text{ K}}$
${V_2} = 6.25{\text{ L}}$
Thus, the volume of air that will be expelled when the gas is cooled to $- {23^ \circ }{\text{C}}$ at the same pressure is $6.25{\text{ L}}$.

Additional Information: Examples of Charles’s law in everyday life are:
Basketball shrinks in the winter season. This is because in the winter season the temperature is lower and the volume also lowers as temperature and volume are in a direct proportion.
The capacity of human lungs decreases in winters. As a result, it becomes difficult for the athletes to perform on a freezing day.
It becomes difficult for a person to jog in winters as the temperature is low.

Note:
Charles’s law describes the expandable behaviour of gases when they are heated. The law states that if a gas is held at a constant pressure, its volume and temperature are in a direct proportion to each other.