Carnot Engine: The Four Steps of the Carnot Cycle Explained

Start at state A (hot, temperature T1). Step 1: Isothermal expansion at T1 - the gas expands slowly touching the hot reservoir, absorbs heat Q1, and temperature stays T1. Step 2: Adiabatic expansion - the gas is now insulated and keeps expanding, so its temperature drops from T1 to T2, with no heat exchange. Step 3: Isothermal compression at T2 - the gas touches the cold reservoir and is compressed, releasing heat Q2, temperature stays T2. Step 4: Adiabatic compression - insulated again, the gas is compressed and its temperature rises from T2 back to T1, returning to the start. Order to remember: isothermal, adiabatic, isothermal, adiabatic.

NCERT explains it simply. To take in and give out heat without wasting energy, heat exchange must happen at a fixed temperature that matches the reservoir - that is what an isothermal step does (no temperature gap, so it stays reversible). So you need one isothermal step for absorbing heat (at T1) and one for releasing heat (at T2). To move between T1 and T2 without touching any reservoir, you must use a step with no heat flow - that is an adiabatic step. You need one adiabatic to cool from T1 to T2 and one to warm from T2 to T1. Two isothermals plus two adiabatics is the only reversible way to build the cycle between just two temperatures.

Only the isothermal steps exchange heat, because adiabatic steps have zero heat flow by definition. Heat Q1 is absorbed from the hot reservoir during Step 1 (isothermal expansion at T1). Heat Q2 is released to the cold reservoir during Step 3 (isothermal compression at T2). No heat enters or leaves during the two adiabatic steps.

NCERT points this out directly. An isochoric step changes temperature by exchanging heat, but a big temperature gap between gas and reservoir makes the process irreversible. To keep it reversible you would need a whole series of reservoirs at every temperature between T2 and T1 - not allowed for an engine that works between only two temperatures. An adiabatic step changes temperature with no heat flow at all, so it needs no extra reservoir and stays reversible. That is why the Carnot cycle uses adiabatic, not isochoric, to bridge the two temperatures.

Because it is a cyclic process - the gas ends exactly where it started (same pressure, volume and temperature). This closes the loop A to B to C to D and back to A. Since it returns to the start, the change in internal energy over one full cycle is zero, and the net work done by the gas equals the area enclosed by the loop.

Yes. Every one of its four steps is reversible - each is quasi-static (very slow) and non-dissipative (no friction). This is why the Carnot engine has the maximum possible efficiency between two given temperatures; any real engine with irreversibility has lower efficiency.

In the NCERT model it is an ideal gas enclosed in a cylinder with a frictionless piston. The gas expands and compresses through the four steps while contacting the hot and cold reservoirs at the right moments.

No. Carnot's key result is that the efficiency of a Carnot engine depends only on the two temperatures T1 and T2, not on the working substance. This is why the formula eta = 1 - T2/T1 has no term for the gas.

Over one full cycle the internal energy change is zero (it returns to the start), so net work W = Q1 - Q2, where Q1 is heat absorbed at T1 and Q2 is heat rejected at T2. This net work equals the area enclosed by the loop on the P-V diagram.

The next step is deriving the efficiency. Applying the isothermal and adiabatic work formulas to the four steps gives the famous result eta = 1 - T2/T1, covered in the Carnot engine efficiency derivation.