# Systems, Walls and State Variables

Physics II · Thermodynamics · https://tryals.app/learn/physics-ii/systems-walls-and-state-variables

## Drawing the Boundary First

Thermodynamics begins by choosing a **system** and calling everything else the **surroundings**. What crosses the boundary is decided by the kind of **wall**:

| Wall | Blocks | Permits |
|---|---|---|
| Adiabatic | Heat | Work |
| Diathermal | Nothing thermal | Heat and work |
| Rigid | Volume change | Heat |
| Impermeable | Matter | Heat and work |

An **isolated** system has adiabatic, rigid, impermeable walls and exchanges nothing at all.

The state of a simple system is fixed by a small number of **state variables**, split by how they scale. **Extensive** variables double when you double the system: volume, internal energy, entropy, mass. **Intensive** ones do not: pressure, temperature, density. Every extensive variable has an intensive partner it pairs with in the energy balance, $P$ with $V$, $T$ with $S$, $\mu$ with $N$.

Dividing one extensive variable by another gives an intensive one, which is why molar and specific quantities are so useful: $v = V/n$ is intensive and describes the substance rather than the sample.

**Thermodynamic equilibrium** requires three conditions at once, thermal (uniform $T$), mechanical (uniform $P$), and chemical (uniform $\mu$). Only in equilibrium do the state variables have well-defined values at all, which is why non-equilibrium states cannot be plotted as points on a $P$-$V$ diagram.

A **quasistatic** process passes through a continuous sequence of equilibrium states, slowly enough that the system is never appreciably out of balance. Every quasistatic path can be drawn as a curve; a violent, irreversible one cannot, and is conventionally shown as a dashed line between endpoints only.

> **Common pitfall:** calling any slow process reversible. Quasistatic is necessary but not sufficient, slow friction is still dissipative. Reversibility additionally requires that no entropy be generated, so that the system *and* its surroundings can both be restored.

## Practice questions

6 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Which conditions must all hold for full thermodynamic equilibrium?

A. Uniform temperature throughout
B. Zero internal energy
C. Uniform chemical potential throughout
D. Uniform pressure throughout

**Answer:** A. Uniform temperature throughout; C. Uniform chemical potential throughout; D. Uniform pressure throughout

**Why:** Thermal, mechanical and chemical equilibrium must hold together. Internal energy has no absolute zero and plays no part in the definition, a system can be in perfect equilibrium at any energy.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/which-conditions-must-all-hold-for-full-thermodynamic-equilibrium

### 2. A process can be quasistatic and still be irreversible.

**Answer:** True

**Why:** True, quasistatic means passing through equilibrium states, which is necessary but not sufficient. A slowly sliding block with friction generates entropy at every step, so it cannot be undone without leaving a trace.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/a-process-can-be-quasistatic-and-still-be-irreversible

### 3. Sort each quantity by whether it is a state function or a path-dependent quantity.

**Answer:**

- State function: Internal energy, Entropy, Pressure
- Path-dependent: Heat transferred, Work done

**Why:** State functions are determined entirely by where the system is now. Heat and work have no value until a *process* is specified, which is exactly why the first law separates them from the internal energy they change.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/sort-each-quantity-by-whether-it-is-a-state-function-or-a

### 4. A system contains 3.0 mol of gas occupying 0.075 m$^3$. Compute the molar volume in m$^3$/mol, to three decimal places.

**Answer:** 0.025 (within ±0.001)

**Why:** $v = V/n = 0.075/3.0 = 0.025$ m$^3$/mol. Dividing one extensive quantity by another gives an *intensive* one, which describes the substance rather than the size of the sample.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/a-system-contains-3-0-mol-of-gas-occupying-0-075-m-compute-the

### 5. Why can a violently irreversible expansion not be drawn as a curve on a $P$-$V$ diagram?

A. The area under the path cannot represent any work done by the gas
B. Such state diagrams can only represent constant-temperature paths
C. The system has no single well-defined pressure during the process
D. Extensive state variables like volume cannot change irreversibly

**Answer:** C. The system has no single well-defined pressure during the process

**Why:** Plotting a point requires uniform, well-defined state variables, that is, equilibrium. A violent process has pressure varying across the gas, so there is no single $P$ to plot. Only the endpoints are defined, which is why such paths are drawn dashed.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/why-can-a-violently-irreversible-expansion-not-be-drawn-as-a-curve-on

### 6. Dividing extensive variables yields intensive ones, so molar volume describes the substance rather than the sample. What follows for two equilibrium sub-volumes partitioned inside the same homogeneous gas container?

A. They retain separate pressures whenever their volume ratios are unequal
B. They can only possess identical molar volumes if their sizes match exactly
C. They must share equal values of molar volume despite differing masses
D. They balance each other by doubling their densities across the divider

**Answer:** C. They must share equal values of molar volume despite differing masses

**Why:** Equilibrium requires uniform intensive fields throughout, so any sub-volume reflects the same molar volume regardless of sample size. Conflating scale-independent properties with extensive totals leads to the false belief that sub-samples require identical masses or separate pressures.

Page: https://tryals.app/practice/physics-ii/systems-walls-and-state-variables/dividing-extensive-variables-yields-intensive-ones-so-molar-volume