Question

A sample of gas at \[35\] degree Celsius and \[1\] atm occupies a volume of \[37.5L\] . At what temperature should the gas be kept, if it is required to reduce the volume to \[3.0\] litre at the same pressure?

Answer 1

Hint: A sample of gas occupies before changes were given, when the volume was changed the temperature also changes as volume and temperature were directly proportional to each other at constant pressure. By substituting the given values, at what temperature the gas should be kept can be determined.
Formula used:
\[\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}\]
\[{V_1}\] is initial volume
\[{T_1}\] is initial temperature
\[{V_2}\] is final volume
\[{T_2}\] is final temperature

Complete answer:
Charles’s law is one of the gas laws that states that at constant pressure and number of moles, volume of a gas is directly proportional to the temperature of a gas.
Given that when a sample of gas at \[35\] degree Celsius and \[1\] atm occupies a volume of \[37.5L\] . and the volume was reduced to \[3.0\] litre at the same pressure.
That means the volume is changed by keeping the pressure constant and it is the same gas. Thus, the number of moles will also be constant.
\[35\] degree Celsius is equal to \[35 + 273 = 308K\]
Substitute the initial and final volume, and temperature in kelvins in the formula:
\[\dfrac{{37.5}}{{308}} = \dfrac{{3.0}}{{{T_2}}}\]
The temperature at \[3.0\] litre \[\left( {{T_2}} \right)\] is \[24.6K\] . In Celsius scale, the temperature will be \[24.6 - 273 = - {248^0}C\]
Thus, the temperature is \[ - {248^0}C\]

Note:
In the above conversion, the obtained temperature is very small, as it is obtained in negative value. The volume and temperature were directly proportional to each other is proved as the volume is reduced by more than \[10\] times, temperature also reduced more than \[10\] times.