An open vessel at `27^@C` is heated untill two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is :

Options

A. `750^(@)C`
B. `500^(@)C`
C. 750 K
D. 500 K

Answer

D

Explanation

`"Air escaped from the vessel "=(2)/(5)`
`"Air remained in vessel "=1-(2)/(5)=(3)/(5)`
`"At constant p and v"`
`n_(1)T_(1)=n_(2)T_(2)`
`n_(1)xx300=(3)/(5)n_(1)xxT_(2)`
`n_(1)xx300=(3)/(5)n_(1)xxT_(1)`
`"or "T_(2)=(5xx300)/(3)=500K`