Thermodynamics & Heat Transfer Cheat Sheet

A printable reference covering heat, temperature, specific heat, latent heat, ideal gases, thermodynamic laws, and heat transfer for grades 10-12.

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Thermodynamics explains how heat, temperature, work, and energy are related in physical systems. This cheat sheet helps students organize the formulas used for heating, cooling, phase changes, gases, and engines. It is especially useful because many problems require choosing the correct equation and using consistent units. Grades 10 through 12 physics students can use it as a quick reference for homework, labs, and test review. The core ideas are conservation of energy, heat transfer, and the behavior of gases. Important formulas include $Q = mc\Delta T$ for temperature change, $Q = mL$ for phase change, and $PV = nRT$ for ideal gases. The first law of thermodynamics is often written as $\Delta U = Q - W$ , where $W$ is work done by the system. Heat transfer can occur by conduction, convection, or radiation, each with its own model and physical meaning.

Key Facts

Heat needed for a temperature change is $Q = mc\Delta T$ , where $m$ is mass, $c$ is specific heat capacity, and $\Delta T$ is the temperature change.
Heat needed for a phase change is $Q = mL$ , where $L$ is the latent heat of fusion or vaporization.
The ideal gas law is $PV = nRT$ , and it can also be written as $PV = Nk_B T$ for $N$ particles.
The first law of thermodynamics is $\Delta U = Q - W$ when $W$ means work done by the system.
Work done by a gas at constant pressure is $W = P\Delta V$ , and more generally it is the area under a $P$ versus $V$ graph.
Thermal efficiency is $e = \frac{W_{out}}{Q_h} = 1 - \frac{Q_c}{Q_h}$ for a heat engine.
Maximum Carnot efficiency is $e_{max} = 1 - \frac{T_c}{T_h}$ , where temperatures must be in kelvins.
Conduction through a flat material is modeled by $P = \frac{kA\Delta T}{L}$ , where $P$ is heat transfer rate.

Vocabulary

Temperature: Temperature is a measure of the average kinetic energy of particles in a substance.
Heat: Heat is energy transferred between objects because of a temperature difference.
Internal energy: Internal energy is the total microscopic kinetic and potential energy of the particles in a system.
Specific heat capacity: Specific heat capacity is the heat required to raise the temperature of $1\,\text{kg}$ of a substance by $1\,\text{K}$ .
Latent heat: Latent heat is the energy absorbed or released during a phase change without a temperature change.
Entropy: Entropy is a measure of energy spreading or disorder, and for a reversible heat transfer it is $\Delta S = \frac{Q_{rev}}{T}$ .

Common Mistakes to Avoid

Confusing heat with temperature is wrong because heat is energy transfer, while temperature measures average particle kinetic energy.
Using Celsius in gas law or Carnot efficiency calculations is wrong because formulas such as $PV = nRT$ and $e_{max} = 1 - \frac{T_c}{T_h}$ require kelvins.
Forgetting phase changes in heating curves is wrong because during melting or boiling the temperature stays constant and the correct formula is $Q = mL$ .
Mixing sign conventions in the first law is wrong because $\Delta U = Q - W$ assumes $W$ is work done by the system, not work done on the system.
Using mass in grams without converting is wrong in SI problems because formulas such as $Q = mc\Delta T$ usually require $m$ in kilograms when $c$ is given in $\text{J}/(\text{kg}\cdot\text{K})$ .

Practice Questions

1 How much heat is needed to raise $2.0\,\text{kg}$ of water from $20^\circ\text{C}$ to $75^\circ\text{C}$ if $c = 4186\,\text{J}/(\text{kg}\cdot\text{K})$ ?
2 How much energy is required to melt $0.50\,\text{kg}$ of ice at $0^\circ\text{C}$ if $L_f = 3.34 \times 10^5\,\text{J}/\text{kg}$ ?
3 A gas absorbs $600\,\text{J}$ of heat and does $250\,\text{J}$ of work on its surroundings. Find $\Delta U$ using $\Delta U = Q - W$ .
4 Explain why a metal spoon feels colder than a wooden spoon at the same room temperature, even though both have the same temperature.