Question

An ideal gas is taken through the cycle \( A \to B \to C \to A \), as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process \( C \to A \) is 

• A. \(-5 \, \text{J}\)
• B. \(-10 \, \text{J}\)
• C. \(-15 \, \text{J}\)
• D. \(-20 \, \text{J}\)

Hint:

In thermodynamic cycles, use the PV diagram to find the work done. The first law of thermodynamics helps relate work, heat, and internal energy.

Answer 1

The Correct Option is A

In thermodynamics, the work done by a gas in a cycle can be found from the area enclosed by the process in a PV diagram. The first law of thermodynamics tells us that the net heat added to the system is equal to the change in internal energy plus the work done by the system. In this case, we are told that the net heat supplied to the gas in the cycle is 5 J. By looking at the PV diagram (not provided here but implied), we can observe that the work done by the gas in the process \( C \to A \) corresponds to the area under the curve in that part of the cycle. This work is negative because the volume decreases. Thus, the work done in the process \( C \to A \) is \( -5 \, \text{J} \), so the correct answer is (A).