Final answer:
Gas 1 will have the greatest increase in thermal energy since it is in a rigid container and all the heat energy contributes to raising its temperature, whereas Gas 2 does work as it expands, using some of the heat energy.
Step-by-step explanation:
When 32,200 J of heat is added to two gases, each in a sealed container, with one gas in a rigid container (Gas 1) and the other in a container where it can expand (Gas 2), there is a difference in how the heat energy is utilized. For Gas 1, in the rigid container, all of the added heat contributes to an increase in the thermal energy because there is no work done on the environment - the volume does not change. In contrast, for Gas 2, some of the heat added is used to do work as the gas expands and lifts the weight - thus pushing out a piston. Therefore, Gas 2 would not have as much increase in thermal energy because part of the energy is converted to work.
The correct answer is A. Gas 1 because it undergoes no change in volume, hence cannot do work on its surroundings, leading to the greatest increase in its thermal energy.