Physics 1A: Thermodynamics

Temperature and heat are not the same thing

Everyday speech uses "heat" and "temperature" interchangeably, but physics distinguishes them sharply and the CBE tests this distinction repeatedly. Get the definitions clean and you will earn several points that most students lose.

• Temperature measures the average kinetic energy of the particles in a substance. It does not depend on how much of the substance you have. A drop of boiling water and an entire pot of boiling water are both at 100 °C.
• Thermal energy (sometimes called internal energy) is the total kinetic energy of all the particles. It depends on how much substance is present. A pot of boiling water contains vastly more thermal energy than a single drop.
• Heat is thermal energy in the process of transferring from a warmer object to a cooler one. It is not a property of an object — it is a flow. You do not have "heat" sitting inside you; you have thermal energy.

Consequence: a small drop of solder at 300 °C and a large bathtub of water at 40 °C — the solder has higher temperature, but the tub of water contains far more thermal energy. Which one would burn you if you touched it? Both could — but the pot of boiling water would give you a much larger burn because it can deliver more heat before its temperature drops.

Temperature scales — Celsius, Fahrenheit, Kelvin

Three temperature scales appear on the CBE. Two of them are convenient (Celsius, Fahrenheit); one is the SI base unit (Kelvin).

• Celsius (°C) — 0 °C is the freezing point of water, 100 °C is the boiling point of water at standard pressure.
• Fahrenheit (°F) — 32 °F freezing, 212 °F boiling. Common in the US.
• Kelvin (K) — the absolute temperature scale. 0 K (absolute zero) is the temperature at which all classical thermal motion would stop. It is 273.15 K below 0 °C. No degree symbol on Kelvin (you write "273 K", not "273 °K").

Conversion formulas from the Physics 1A formula chart:

T_F = (9/5) · T_C + 32     T_C = (5/9) · (T_F − 32)     T_K = T_C + 273.15

Careful with ΔT: a temperature change of 10 °C is also 10 K (the scales are offset but have the same step size), but only 18 °F (Fahrenheit steps are smaller).

Specific heat capacity — how much heat to change temperature

Different substances require different amounts of heat to change temperature by the same amount. Water, for example, is unusually resistant to temperature change — you have to dump a lot of heat into water to warm it, and it also holds that heat well. This is why lakes moderate the temperature of nearby land, and why coastal cities have milder climates than inland ones at the same latitude.

The relationship is:

Q = m · c · ΔT

Where Q is the heat transferred (in joules), m is the mass (kg or g), ΔT is the temperature change, and c is the specific heat capacity — a property of the material. Water has c ≈ 4,186 J/(kg·°C), or about 4.18 J/(g·°C). Metals have much lower c values — copper is around 385 J/(kg·°C), and aluminum is about 900 J/(kg·°C). Adding the same amount of heat to equal masses of copper and water raises the copper’s temperature much more.

Typical CBE question setup: "How much heat is required to raise the temperature of 500 g of water from 20 °C to 80 °C?" Answer: Q = 500 · 4.18 · (80 − 20) = 500 · 4.18 · 60 ≈ 125,400 J. The distractor to watch out for is using the final temperature (80) instead of the change (60), which would give about 167,200 J. Always compute ΔT first.

Three ways heat travels

Thermal energy transfers between objects through three mechanisms. The CBE will show you a scenario and ask you to identify which is at work.

• Conduction — heat transferred through direct contact between materials. Touching a hot pan handle. Heat moving through a metal spoon in a bowl of soup. Requires physical contact between the source and receiver.
• Convection — heat transferred by bulk motion of a fluid (liquid or gas). Warm air rising above a heater and cool air sinking to replace it. Water circulating in a boiling pot. Requires a fluid (does not work through solids or vacuum).
• Radiation — heat transferred as electromagnetic waves. Sunlight warming your skin. A campfire’s heat reaching you across the air. Radiation is the only mechanism that works through a vacuum — which is why the Sun can warm the Earth across 150 million kilometers of empty space.

A classic CBE trap: a metal spoon left in a hot bowl of soup. Heat travels along the spoon from the soup to the handle. Which mechanism? Conduction (direct contact through the metal). The soup itself heats via convection within its liquid, and any warmth you feel above the bowl without touching it is radiation.

The laws of thermodynamics

The CBE tests the first and second laws conceptually. The zeroth is background context.

Zeroth law — the definition of temperature

If object A is in thermal equilibrium with object B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. This sounds trivially obvious, but it is what lets us assign each object a single "temperature" that we can compare. Without this law, temperature would not be a well-defined property.

First law — conservation of energy including heat

The total energy of an isolated system is constant. Energy can be transformed between kinetic, potential, thermal, chemical, or electrical forms, but the total cannot be created or destroyed. When heat Q flows into a system and the system does work W on its surroundings, the change in the system’s internal energy is:

ΔU = Q − W

This is the energy-conservation principle from earlier lessons, extended to include heat as a form of energy transfer. On the CBE, first-law questions usually appear as bookkeeping: "How much heat flowed if the internal energy rose by X and the system did Y of work?" Add or subtract carefully.

Second law — entropy always increases

Every real-world process increases the total entropy — a measure of disorder or unavailable energy — of an isolated system. A cup of hot coffee cools to room temperature; the reverse (a cool cup spontaneously heating itself) never happens. Ice cubes melt; a puddle of water does not spontaneously refreeze. This one-way arrow of time is embedded in the second law of thermodynamics.

Practical consequences the CBE tests:

• No engine is 100% efficient. Some heat always escapes as waste to a cold reservoir. You can approach but never reach total efficiency.
• Heat flows spontaneously from hot to cold, never the reverse without external work. A refrigerator moves heat from cold interior to warm exterior — but it requires electrical work to do so.

Heat engines and efficiency

A heat engine takes in heat from a hot reservoir (Q_H), converts some of it to useful work (W), and expels the rest as waste heat to a cold reservoir (Q_C). Efficiency is the fraction of input heat that becomes useful work:

e = W / Q_H

Since Q_H = W + Q_C (first law), efficiency can also be written as e = 1 − Q_C/Q_H. An engine that absorbs 1,000 J and produces 300 J of work has efficiency 0.30 or 30% — and dumps 700 J as waste heat to the cold reservoir.

The second law places a hard limit on how efficient any heat engine can be — the Carnot limit, based on the temperatures of the two reservoirs. Real engines fall well short of this limit. Gasoline engines are typically around 20-30% efficient. Steam power plants around 40%. There is no clever engineering that lets you exceed the second law.

Thermal expansion

Nearly all materials expand when heated. The change in length is proportional to the original length and the temperature change:

ΔL = α · L · ΔT

Where α (the coefficient of thermal expansion) depends on the material. Metals have values of about 10 to 25 × 10⁻⁶ per °C — small, but they add up when the object is large. This is why railroad tracks have expansion joints (gaps to accommodate hot-weather lengthening), bridges have expansion plates, and drinking glasses can crack when hit with sudden hot water. A thermometer works on the same principle: the mercury or alcohol expands linearly with temperature and rises in a narrow tube.

Water is an important exception: from 0 °C to 4 °C, it actually contracts as it warms (an anomaly caused by hydrogen bonding). Above 4 °C, it expands normally. This is why ice floats, and why lakes freeze from the top down rather than the bottom up.

Where students lose points

• Using final temperature instead of ΔT in Q = mcΔT. Always compute the change first.
• Confusing temperature with heat. Temperature is an average per particle; heat is the total energy in transit.
• Assigning "heat" as something an object has. Objects have thermal energy. Heat is thermal energy moving between objects.
• Claiming that heat can flow spontaneously from cold to hot. Second law forbids this without external work.
• Assuming 100% efficient engines are possible with enough engineering. The second law puts an unconditional upper bound.
• Mixing up the three transfer mechanisms. Conduction requires contact through matter; convection requires bulk fluid motion; radiation works through vacuum.

Worked example — mixing hot and cold water

500 g of water at 80 °C is poured into a beaker containing 300 g of water at 20 °C. Assuming no heat is lost to the environment, what is the final temperature of the mixture?

Step 1 — Set up the heat balance. Heat lost by the hot water = heat gained by the cold water.

m_H · c · (T_H − T_f) = m_C · c · (T_f − T_C)

Step 2 — c cancels out (same substance). Solve for T_f:

500 · (80 − T_f) = 300 · (T_f − 20)

Step 3 — Expand and solve. 40,000 − 500 T_f = 300 T_f − 6,000. Combine: 46,000 = 800 T_f. So T_f = 57.5 °C.

Sanity check: the answer should lie between 20 and 80, and it should be closer to 80 because the hot water has more mass. 57.5 °C sits closer to 80 than to 20 — consistent. If you got 50 °C exactly, you may have used a simple average and ignored the mass weighting; that is a common CBE distractor.

Check yourself

1. Explain in one sentence each: temperature, thermal energy, and heat.
2. Which temperature scale must you use when computing ΔT for the ideal gas law? Which can you use for Q = mcΔT?
3. Give an everyday example of each of the three heat transfer mechanisms.
4. State the second law of thermodynamics in your own words. Give one everyday process it forbids.
5. An engine absorbs 800 J and produces 240 J of work. What is its efficiency, and how much waste heat does it produce?
6. Why do railroad tracks have expansion joints?

(Answer to #5: e = 240/800 = 0.30 or 30%. Waste heat Q_C = 800 − 240 = 560 J.)

Practice with CBE-style questions

Thermodynamics questions on the CBE cluster around specific heat calculations, transfer-mechanism identification, and efficiency computations. Work through the practice bank filtered by Thermodynamics — every question includes a step-by-step solution and identifies which conceptual mistake each distractor represents.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(6)(E), (c)(6)(F), (c)(6)(G). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.