A 2.0 mol ideal gas system is maintained at a constant volume of 4.0 L. If 100 J of heat is added, what is the work done on the system

Work done on the system is zero , hence no work is done since the process is isochoric. There is no work done if the volume remains unchanged. (Though the temperature rises, work is only accomplished when the volume of the gas changes.)

Explanation:

ISOCHORIC PROCESS - An isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, is a thermodynamic process in which the volume of the closed system undergoing the process remains constant through the process. The heating or cooling of the contents of a sealed, inelastic container is an example of an isochoric process. The thermodynamic process is the addition or removal of heat, the closed system is established by the isolation of the contents of the container, and the constant-volume condition is imposed by the container's inability to deform. It should be a quasi-static isochoric process in this case.

Hence , the work done in the system is zero.

c. heat could easily travel through the molecules in the air and escape/enter the flask. removing the air slows down the heat transfer.  

false

because it does not have the potential to be entirely used up