Question

Choose the correct statement for processes A & B shown in figure.

• A. \( PV^n = k \) for process B and \( PV = k \) for process A.
• B. \( PV = k \) for process B and A.
• C. \( P^{n-1} = k \) for process B and \( T^n = k \) for process A.
• D. \( T^n P^{n-1} = k \) for process A and \( PV = k \) for process B.

Answer 1

The Correct Option is A, C

To determine the correct statements about the processes represented in the graph, we need to analyze the nature of processes A and B.

Process A is typically an isothermal process, which means that the temperature remains constant (\( T = \text{const} \)).
For an isothermal process, the equation \( PV = nRT \) holds true, indicating that the product of pressure and volume is constant.

Process B appears to be adiabatic since the slope is steeper than that of an isothermal process, which indicates that heat is not exchanged with the environment.
The adiabatic process is described by the equation \( PV^\gamma = \text{const} \), where \( \gamma = \frac{C_p}{C_v} \) is the ratio of specific heats.

Statements Analysis:

Statement (1): \( PV^n = k \) for process B is correct if process B follows an adiabatic path. \( PV = k \) for process A is also valid as it suggests constant temperature.

Statement (2): This statement does not hold true based on the analysis of processes A and B.

Statement (3): \( P^{n-1} = k \) for process B is valid for an adiabatic process, while \( T^n = k \) is a general representation for process A under isothermal conditions.

Statement (4): This statement is misleading; the relationship does not generally hold in the given form.

Thus, the correct statements regarding processes A and B are:

(1) and (3).