Thermodynamics

This is a problem involving the ideal gas law. The ideal gas law is
given by:
where: is the pressure, is the volume, is the number of moles of gas, is the gas constant, is the temperature in Kelvin. We are given:
Initial pressure , Initial volume , Initial temperature , Final pressure , Final volume . Using the ideal gas law and the proportionality of the variables for a constant amount of gas, we can use the combined gas law: Substituting the known values: Canceling the common terms and : Now, solve for : Thus, the final temperature is 1200 K, which corresponds to (D).

Step 1: Understand the path of the gas in the P-V diagram.
The gas undergoes a cyclic process represented by the ABCDA path in the P-V diagram. In such a cycle, the work done is equal to the area enclosed by the path.
Step 2: Calculate the work done.
For the
given path, the area enclosed by the rectangle formed in the P-V diagram corresponds to the work done. The work done is:
where and are the pressure and volume at the initial state.
Step 3: Conclusion.
Thus, the work done by the gas is .
Conclusion:
The correct answer is (B) .