An open vessel at `27^@C` is heated until three fifth of the air in it has been expelled। Assuming volume of vessel constant find the temperature to which the vessel has been heated

Explanation

Given the vessel is open, its volume remains constant. Therefore, the pressure will also be constant. We have the following two general gas equation:
`PV=n_(1)RT_(1)` and `PV=n_(2)RT_(2)`
where `n_(1)`, `n_(2)` are the numbers of moles and `T_(1)`, `T_(2)` are the temperatures.
Thus,
`n_(1)RT_(1)=n_(2)RT_(2)`
or `n_(1)T_(1)=n_(2)T_(2)`
Let the initial number of moles be `1`.
Number of moles remaining `=1-(3)/(5)=(2)/(5)=0.4`
`T_(1)=27+273=300 K`, `T_(2)=?`
Putting the values in above equation, we get
`1xx300=0.4xxT_(2)`
`T_(2)=(300xx1)/(0.4)=750 K`
Thus, the required temperature is `750-273=477^(@)C`.