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

An open vessel at 27^@C is heated until three fifth of the air in it h

1.	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
Answer» Solution :When an open vessel is HEATED, its volume and PRESSURE may be regarded as constant। Suppose the pressure and volume in the vessel are P and V respectively। If `n_1` represents the number of moles of the gas in the vessel before heating and `n_2` after heating, we have (according to the ideal gas equation), `PV=n_1 RT_1 "" ...(i)` and `PV = n_2 RT_2"" ...(ii)` where `T_1`is the temperature of the gas before heating and `T_2` after heating. Dividing Eqs. (i) by (ii), we have `1 = (n_1 T_1)/(n_2 T_2) "or" n_2/n_2 = T_1/T_1""..(iii)` In the present case, `T_1= 273 + 27 = 300 K " and " T_2` = ? Since on heating three fifth air is EXPELLED, therefore `n_2 = n_1 - (n_1 xx 3/5 ) = 2/5 n_1` Substituting the values is Eq। (iii), we have `(2/5n_1)/n_1 =300/T_2` `:. "" T_2 = 750K` Hence, the vessel has been heated to `750 - 273 = 477^@C`.