If a sealed syringe that contains some gas in heated in which direction will the syringe plunger move

The movement of the plunger will take place in outward direction elevating the volume in the syringe.  

The upsurge in heat will lead to an elevation in temperature of the gas particles. This elevation in temperature will lead to an elevation in motion. The elevation in motion (kinetic energy) will result in an increase in pressure within the syringe. This elevation in pressure will further result in an upsurge in the volume of the syringe.  

According to Charle's law, the temperature and volume are directly equivalent, that is, as the temperature increases the volume will also increase. Thus, an increase in temperature and heat will result in an increase in volume making the plunger to move outward.