1. why was it necessary for boyle to seal one end of his j-tube?

2. what would have happened if boyle had allowed the temperature of the trapped air sample to change as he added mercury to the tube?

1. It was necessary for Boyle to seal one end of the J-tube as it allowed him to examine the pressure-volume relationship without complications from other elements, like changes in the amount of gas or temperatures. He changed the volume and the pressure of the gas and came to know that the volume of a fixed mass of a gas is inversely proportional to the pressure at constant temperature.  

2. If Boyle would have permitted the temperature of the trapped air sample to change as he supplemented mercury to the tube, the temperature would not have remained same and thus, he would not be able to make the supposition of constant temperature in his calculations.