# Reversibility and Irreversibility

Physics II · Thermodynamics · https://tryals.app/learn/physics-ii/reversibility-and-irreversibility

## The Test for Undoing

A **reversible** process can be run backwards so that both the system *and* its surroundings return to their original states, leaving no trace anywhere. The test includes the surroundings, that is what makes it strict.

Reversibility requires the process to be quasistatic **and** free of dissipation. Both conditions matter. A slow process with friction is quasistatic yet irreversible, because the friction heat cannot be gathered up and turned back into ordered motion.

The standard sources of irreversibility all share a structure, each involves a **finite gradient** driving a spontaneous change:

| Source | Finite gradient |
|---|---|
| Heat flow across a temperature difference | $\Delta T$ |
| Free expansion into a vacuum | $\Delta P$ |
| Friction and viscous dissipation | Velocity difference |
| Mixing of different substances | $\Delta$ composition |
| Chemical reaction proceeding | $\Delta \mu$ |

Reversible processes are the limiting case as every gradient tends to zero, which is why they are also **infinitely slow** and deliver zero power. They are an idealisation, and useful precisely because they bound what is achievable: reversible work is the maximum extractable, and reversible heat pumping is the cheapest possible.

The asymmetry is directional. Work converts entirely into heat with no difficulty at all — stir a fluid, rub two surfaces — but heat cannot be wholly converted back into work. This one-way character is the empirical content behind the second law, and it holds no matter how carefully the machinery is built.

> **Common pitfall:** thinking irreversibility means "cannot be undone at all". A gas that expanded freely can certainly be recompressed. The point is that doing so costs work and dumps heat into the surroundings, so the *universe* does not return to its earlier state, only the system does.

## Practice questions

5 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. What distinguishes a reversible process from a merely quasistatic one?

A. A reversible process need not pass through equilibrium states
B. A quasistatic process cannot be plotted on a P-V diagram
C. A quasistatic process must be entirely free from friction
D. A reversible process also generates no entropy anywhere

**Answer:** D. A reversible process also generates no entropy anywhere

**Why:** Quasistatic means passing through equilibrium states; reversible additionally requires no dissipation, so that the surroundings can be restored too. Slow friction satisfies the first and fails the second.

Page: https://tryals.app/practice/physics-ii/reversibility-and-irreversibility/what-distinguishes-a-reversible-process-from-a-merely-quasistatic-one

### 2. Sort each process by whether it is reversible in principle or irreversible.

**Answer:**

- Reversible in the limit: Infinitely slow isothermal expansion with no friction, Quasistatic compression by a frictionless piston
- Always irreversible: Warmth spreading between bodies at unequal temperature, Free expansion into a vacuum, Two gases mixing spontaneously

**Why:** Reversible processes are the zero-gradient limit. Every irreversible one here has a finite driving difference — of temperature, pressure or composition — and each generates entropy as it proceeds.

Page: https://tryals.app/practice/physics-ii/reversibility-and-irreversibility/sort-each-process-by-whether-it-is-reversible-in-principle-or

### 3. A freely expanded gas can never be returned to its original volume.

**Answer:** False

**Why:** False, you can certainly recompress it. Irreversibility means the *surroundings* cannot also be restored: the recompression costs work and dumps heat, so the universe keeps a permanent record even though the system does not.

Page: https://tryals.app/practice/physics-ii/reversibility-and-irreversibility/a-freely-expanded-gas-can-never-be-returned-to-its-original-volume

### 4. Why is a reversible process incapable of delivering any power?

A. Its net work output is completely balanced by internal heat loss
B. It requires infinitesimal gradients, so it takes infinite time
C. Continuous friction and viscous drag dissipate all useful energy
D. It maintains strict equilibrium, preventing any net work output

**Answer:** B. It requires infinitesimal gradients, so it takes infinite time

**Why:** Reversibility is the zero-gradient limit, and zero gradient means zero rate. The work done is actually the *maximum* possible, it is simply delivered infinitely slowly, so the power is zero.

Page: https://tryals.app/practice/physics-ii/reversibility-and-irreversibility/why-is-a-reversible-process-incapable-of-delivering-any-power

### 5. Reversibility tests whether the surroundings as well as the system can be restored without trace. What follows from this total accounting when evaluating an irreversible change?

A. Both system and surroundings remain permanently stuck in their altered states
B. The system cannot be returned to its initial state by any sequence of steps
C. Surroundings can fully recover provided the restoration operates quasistatically
D. Restoring the system alone necessarily leaves an indelible imprint elsewhere

**Answer:** D. Restoring the system alone necessarily leaves an indelible imprint elsewhere

**Why:** Confusing system recovery with total recovery is common: any state can be revisited, but unravelling dissipation always demands external work that leaves heat in the surroundings. Absolute irreversibility does not mean a system is trapped forever.

Page: https://tryals.app/practice/physics-ii/reversibility-and-irreversibility/reversibility-tests-whether-the-surroundings-as-well-as-the-system