# Problem-Solving: Waves, Fluids, and Thermodynamics

Physics I · Principles of Waves, Fluids and Thermodynamics · https://tryals.app/learn/physics-i/problem-solving-waves-fluids-and-thermodynamics

## Problem-Solving: Waves and Fluids

The same deep patterns govern wildly different systems, from earthquake tremors to aircraft lift. Capstone success is entirely about **recognizing** which principle is in play.

Before computing, classify your system. Real problems never announce their chapter.

| Domain | Governing Principle | Key Formula | Common Pitfall |
| --- | --- | --- | --- |
| **Waves** | Speed & Harmonics | $v = f\lambda$ | Missing boundary conditions |
| **Fluids (Static)** | Pressure depth | $P = P_0 + \rho g h$ | Using gauge pressure in gas laws |
| **Fluids (Flow)** | Continuity & Energy | Bernoulli's Eq. | Forgetting to convert to Kelvin |

**Strategy:** Always identify the system, list knowns with units, and solve algebraically before plugging in numbers.

## Thermodynamics & Sanity Checks

Energy ledgers track heat, work, and entropy. Always respect sign conventions for **work ($W$)** and **heat ($Q$)**.

| Domain | Governing Principle | Key Formula | Common Pitfall |
| --- | --- | --- | --- |
| **Heat** | Temp & Phase Change | $Q = mc\Delta T$, $mL$ | Ignoring sign conventions |
| **Engines** | Efficiency limit | $\eta = W/Q_H$ | Confusing $Q_H$ with $Q_C$ |
| **Entropy** | Disorder ledger | $\Delta S = \int dQ/T$ | Non-Kelvin absolute temps |

**Dimensional analysis** is your ultimate sanity check. If the units do not match your target variable, the algebra failed long before the arithmetic did.

## Practice questions

6 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. A power plant boils water with coal, spins a turbine, and lights your lamp. Order the energy conversions, and note where the second law takes its cut.

**Answer:**

1. Chemical energy in coal is released as heat by combustion
2. Heat turns water into high-pressure steam (thermal energy)
3. Steam expands and does work spinning the turbine
4. The second law forces part of the heat out through cooling towers
5. The generator converts rotational work into electrical energy

**Why:** Every heat engine on Earth follows this chain, and every one pays the second-law toll: heat cannot become work at 100%. The billowing cooling towers are not pollution, they are thermodynamics made visible.

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/a-power-plant-boils-water-with-coal-spins-a-turbine-and-lights-your

### 2. Waves, fluids and thermodynamics all use conservation laws, but the useful conserved quantity differs. How can you tell which one to reach for?

A. The number of dimensions in which the problem is posed
B. The units the question is asked in
C. What the system exchanges with its surroundings
D. Whether the process is fast or slow compared with equilibration

**Answer:** C. What the system exchanges with its surroundings

**Why:** A quantity is conserved when nothing carries it across the boundary. Identifying the system and its boundary first is what selects the law, which is why "what is the system?" is the first question in every one of these problems.

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/waves-fluids-and-thermodynamics-all-use-conservation-laws-but-the

### 3. Bernoulli's equation $P + \frac{1}{2} \rho v^{2} + \rho gh = \text{constant}$ applies to ideal, incompressible, steady, irrotational flow along a streamline.

**Answer:** True

**Why:** Bernoulli's equation holds under these four conditions; real fluids deviate due to viscosity and turbulence.

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/bernoullis-equation-p-1-2-v-gh-constant-applies-to-ideal

### 4. Which of the following quantities are conserved in an isolated system?

A. Angular momentum
B. Total energy
C. Entropy (it can only increase, not stay the same)
D. Linear momentum

**Answer:** A. Angular momentum; B. Total energy; D. Linear momentum

**Why:** Energy, linear momentum, and angular momentum are conserved in isolated systems. Entropy can increase (second law).

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/which-of-the-following-quantities-are-conserved-in-an-isolated-system

### 5. Complete the following passage by choosing the correct terms from the word bank.

**Answer:** Conservation of energy is central to physics. In thermodynamics, $\Delta U = Q - W$; in fluid flow, Bernoulli shows kinetic plus **pressure** plus potential energy is constant; in wave motion, energy flux is proportional to the square of the **amplitude**.

**Why:** Energy conservation unifies mechanics, fluid dynamics, and wave physics.

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/complete-the-following-passage-by-choosing-the-correct-terms-from-the

### 6. Sort each formula into its domain: Waves, Fluids, or Thermodynamics.

**Answer:**

- Waves: $v = f\lambda$, $y = A \sin(kx - \omega t)$
- Fluids: P + $\frac{1}{2} \rho v^{2}$ = const, $A_{1}v_{1} = A_{2}v_{2}$
- Thermodynamics: $\Delta U = Q - W$, η = 1 − $T_c$/$T_h$

**Why:** Each formula encodes a core idea from its respective subdiscipline.

Page: https://tryals.app/practice/physics-i/problem-solving-waves-fluids-and-thermodynamics/sort-each-formula-into-its-domain-waves-fluids-or-thermodynamics