The question involves the first law of thermodynamics where the change in internal energy is affected by the heat added and the work done. Specifically, when heat is added along path CA with work details not provided, and a comparison with path CBA where work is zero during a volume-constant segment.
Step-by-step explanation:
The student's question relates to the thermodynamics of an ideal gas and involves applying the first law of thermodynamics. This law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W), which can be mathematically represented as ΔU = Q - W.
(a) To determine the change in internal energy of the gas when 2042 J of heat is added and the gas expands along the direct path CA, we use the first law of thermodynamics. Since the question only provides the heat added and does not specify the work done, we cannot calculate the exact change in internal energy without additional information about the work.
(b) To calculate the heat required for the same change in internal energy along path CBA, it's important to understand that the work done during the vertical portion BC is zero since the volume is constant and thus no work is performed (W = 0). Therefore, the change in internal energy would ideally be the same as the heat added while taking the path CBA, similar to path CA. However, different paths can result in different amounts of work done, which would affect the amount of heat required to achieve the same change in internal energy. Without specific values or areas under the path curves, we can't provide exact heat quantities for path CBA.