Question

According to Charles law, the lowest possible temperature is (in ${}^ \circ C$):

Answer 1

Hint: Charles law tells that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure. When the pressure exerted on a dry gas sample is kept constant, the Kelvin temperature and volume would be in direct proportion.

Complete step-by-step answer:
There are three main gas laws: Charles' Law, Boyle's Law, and Avogadro's Law.
Charles' Law states that the volume of a fixed mass of gas reduces as it is cooled and increases when the temperature rises.
Boyle's Law tells that the pressure of a given mass of an ideal gas is inversely proportional to the volume at a constant temperature.
Avogadro's Law states that equivalent volumes of different gases produce an equal number of molecules at the same temperature and pressure.

According to Charles law, the volume of the gas rises by $\dfrac{1}{{273}}$ times its initial volume at $0{}^ \circ C$with every degree increase in temperature provided that the pressure remains constant.
${V_0}$ represents the initial volume at zero degrees Celsius and $V$ represents the final volume.
$V = {V_0} + \left( {\dfrac{t}{{273}}} \right){V_0}$
Now, on taking ${V_0}$ common in the right-hand side of the equation, we get,
$V = {V_0}\left[ {1 + \left( {\dfrac{t}{{273}}} \right)} \right]$
When $t = - 273{}^ \circ C$ , we get,
$
  V = {V_0}\left[ {1 + \left( {\dfrac{{ - 273}}{{273}}} \right)} \right] \\
   \Rightarrow V = {V_0}\left[ {1 - \left( {\dfrac{{273}}{{273}}} \right)} \right] \\
 $
${V_0}$ becomes zero on multiplying with $\left[ {1 - \dfrac{{273}}{{273}}} \right]$​
$ \Rightarrow V = 0$
At $ - 273{}^ \circ C$ , the volume of any gas is equal to zero. The volume would be negative below this temperature, which is not possible.

As a result, according to Charles law, the lowest temperature possible is $ - 273{}^ \circ C$.

Note: An ideal gas is one that obeys the gas laws under all temperature and pressure conditions. Though there are no ideal gases, certain gases behave like ideal gases in certain conditions. Understanding gas behaviour and simplifying calculations of gas properties are also helped by the concept of an ideal gas.