Physics · Thermodynamics · NEET
Internal energy U is a state function. This means its value depends only on the current state of the gas (for an ideal gas, only on its temperature), not on the path taken. In a cyclic process the gas comes back to the same state it started from, so its temperature is the same and U is the same. The change is dU = U(final) - U(initial) = 0. It does not matter how curvy or complicated the path was in between.
No. dU = 0 does NOT mean W = 0. From the first law Q = dU + W, setting dU = 0 gives Q = W. So the gas can absorb heat and do net work equal to that heat over the full cycle. Work is zero only for a special path (like a single isochoric line), not for a real loop that encloses an area.
Work done by a gas in one step is W = area under that part of the curve (W = integral of P dV). In a cycle the gas expands on one part (positive work, area under the upper path) and is compressed on the return part (negative work, area under the lower path). When you subtract the return work from the forward work, the areas below both paths cancel and only the area trapped inside the loop is left. So net work = area enclosed by the loop.
Look at the direction the loop is traced on the P-V graph. Clockwise loop means positive net work (the gas does work on the surroundings, like a heat engine). Anticlockwise loop means negative net work (work is done on the gas, like a refrigerator). The size of the work is the same area either way; only the sign flips with direction.
Only for the WHOLE cycle. For a single step, dU is usually not zero, so Q and W differ in that step. It is only when you add up the complete loop that dU cancels to zero and the totals satisfy Q(net) = W(net) = area of the loop.
One mole of an ideal monatomic gas undergoes a cyclic process (rectangle a to b to c to d in the P-V plane, with P between 100 and 300 N/m^2, and V between 2 and 5 m^3). The total heat supplied to the gas is:
A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A cyclic process is a series of changes after which the gas returns to its exact initial state (same pressure, volume and temperature). On a P-V graph it appears as a closed loop.
Internal energy is a state function, so it depends only on the state of the gas, not the path. Since the final state equals the initial state in a cycle, dU = U(final) - U(initial) = 0.
The area enclosed by the loop on a P-V diagram equals the net work done in one complete cycle, which also equals the net heat exchanged since Q = W when dU = 0.
A clockwise loop means positive net work is done by the gas (it behaves like a heat engine, absorbing heat and doing work). An anticlockwise loop means net work is done on the gas (like a refrigerator).
Yes. For a heat engine running on a cycle, the useful work output equals the area of the loop. Efficiency is that work divided by the heat absorbed from the hot source.
