Question

figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be:

• A. 460 J
• B. 300 J
• C. 380 J
• D. 500 J

Answer 1

The Correct Option is A

 To understand the problem, we need to analyze the thermodynamic processes involved when a gas transitions from state A to state C, either directly or via an intermediate state B. The problem gives us two processes: AB followed by BC, and asks about the heat absorbed in process AC.

Concept:

This problem is based on the First Law of Thermodynamics, which can be stated as:

\(Q = \Delta U + W\),

where \(Q\) is the heat added to the system, \(\Delta U\) is the change in internal energy, and \(W\) is the work done by the system.

Step-by-Step Analysis:

1. In process AB, 400 J of heat is added. Assume the internal energy changes by \(\Delta U_{AB}\) and the work done is \(W_{AB}\).
2. In process BC, an additional 100 J of heat is added with a change in internal energy \(\Delta U_{BC}\) and work done \(W_{BC}\).
3. Overall, for process ABC (combining AB and BC), apply conservation of energy:

\(Q_{ABC} = Q_{AB} + Q_{BC} = 400 \text{ J} + 100 \text{ J} = 500 \text{ J}\)

1. Since the initial state A and the final state C are the same regardless of the path taken, \(\Delta U_{AC} = \Delta U_{AB} + \Delta U_{BC}\).
2. For path AC, we must assume a certain amount of work done, \(W_{AC}\), such that:

\(Q_{AC} = \Delta U_{AC} + W_{AC} = 460 \text{ J}\)

Conclusion:

The heat absorbed by the system in the direct process AC is 460 J. This assumes the system does less work or there is less change in internal energy directly compared to the path ABC. The answer is therefore 460 J, which matches the correct option given.