Thermodynamics Study Guide

Level High SchoolReview time ~12 hours

Thermodynamics governs engines, weather, and the fate of the universe — all from a few laws about energy and disorder. Keep heat and temperature distinct, temperature in kelvin, and the sign convention written down, and the subject behaves.

Key formulas

Ideal Gas Law — PV = nRT

Pressure times volume equals moles times the gas constant times absolute temperature.

Kinetic Energy Formula — KE = ½mv²

Kinetic energy equals one-half times mass times velocity squared.

Specific Heat — Q = mcΔT

Heat transferred equals mass times specific heat times temperature change.

Thermal Efficiency — η = W/Qh

Thermal efficiency equals useful work output divided by heat input.

Work Formula — W = Fd

Work equals force times distance moved in the direction of the force.

Topic checklist

Heat versus temperature

Define temperature (average kinetic energy) versus heat (energy in transit).
Convert between Celsius and Kelvin ( $K = °C + 273.15$ ) for all gas-law work.
Explain why two objects at the same temperature can hold different amounts of heat.

Specific heat

Use $Q = mc\Delta T$ with correct units for $c$ .
Know water's high specific heat ( $4186\ \mathrm{J/(kg\cdot K)}$ ) and why it stabilizes climates.
Distinguish heat capacity from specific heat capacity.

Ideal gases

Apply $PV = nRT$ with $T$ always in kelvin.
Use $R = 8.314\ \mathrm{J/(mol\cdot K)}$ with matching SI units.
Solve gas problems by listing $P, V, n, T$ before and after.

First law of thermodynamics

State the first law: $\Delta U = Q - W$ (watch your sign convention).
Identify isothermal, adiabatic, isobaric, and isochoric processes.
Track work as the area under a $P$ - $V$ curve.

Entropy and the second law

Define entropy as the count of microscopic arrangements.
State the second law: entropy of an isolated system never decreases.
Explain why heat flows hot to cold without being told to.

Heat engines

Compute thermal efficiency $\eta = W/Q_h$ .
Know the Carnot limit $\eta_{max} = 1 - T_c/T_h$ (kelvin!).
Explain why no engine reaches 100% efficiency.

Common mistakes

Mistake: Using heat and temperature as synonyms.

Fix:

Heat is energy moving because of a temperature difference; temperature measures average molecular kinetic energy. A sparkler is hot but holds little heat; a bathtub is cooler but holds far more. Use the words precisely.

Mistake: Plugging Celsius into the ideal gas law.

Fix:

Gas laws demand absolute temperature. 20 °C is 293 K, and doubling Celsius does not double the kelvin value. Convert first, calculate second — every time.

Mistake: Forgetting latent heat during phase changes.

Fix:

$Q = mc\Delta T$ only covers temperature change. Melting or boiling needs latent heat ( $Q = mL$ ) with no temperature change at all. Check whether the problem crosses a phase boundary.

Mistake: Mixing sign conventions in the first law.

Fix:

Pick one convention and write it down: physics often uses $\Delta U = Q - W$ (W = work done BY the system), chemistry the opposite. Marks depend on consistency, not on which you chose.

Mistake: Using Celsius in the Carnot efficiency.

Fix:

The Carnot formula needs the ratio of absolute temperatures. $1 - 300/600 = 0.50$ is right; $1 - 27/327$ is wrong. Kelvin always.

Exam tips

Convert to kelvin before touching any gas-law or Carnot calculation.
List knowns as $P, V, n, T$ pairs (before/after) for gas problems.
For first-law problems, write your sign convention at the top of the work.
Efficiency questions: identify $Q_h$ (heat in) versus $W$ (work out) before dividing.