IMAT Physics · Free notes

Heat and Thermodynamics: Calorimetry, Gases and the Laws

Heat and Thermodynamics has 13 past questions since 2011, and the ministry papers from 2023 on have asked 3 of them. Most are short calculations: rearranging Q = mcΔT, finding a latent heat, or applying a gas law. The rest ask which statements are true about a gas held at constant temperature or a solid that is melting, so you need the reasons as well as the formulas. The difficulty is in the bookkeeping: kelvin rather than Celsius, seconds rather than minutes, and no missing term in an energy balance.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

9 formulas · 3 reference tables · 17 gotchas across all subtopics — the exam-eve cheat-sheet

Temperature, Heat and How Heat Moves

Formulas (2)

Temperature, heat and the Kelvin scale · Celsius to kelvin $T\,(\text{K}) = \theta\,(^\circ\text{C}) + 273$
Thermal expansion of solids and liquids · Linear expansion $\Delta L = \alpha L_0 \Delta T$

Reference tables (1)

Heat transfer: conduction, convection and radiation3 rows

Mechanism	How the energy moves	Needs a medium?	Everyday example
Conduction	Vibrating particles and free electrons pass energy to neighbours	Yes; works best in solids, especially metals	The handle of a metal pan getting hot
Convection	Warm, less dense fluid rises and cooler fluid sinks, forming a current	Yes; only liquids and gases	Warm air rising above a radiator
Radiation	Electromagnetic waves, mainly infrared	No; it crosses a vacuum	Sunlight warming the Earth through space

Watch out for (4)

A temperature change is not converted by adding 273
→ Temperature, heat and the Kelvin scale
Heat and temperature are different quantities
→ Temperature, heat and the Kelvin scale
Feeling colder does not mean a lower temperature
→ Heat transfer: conduction, convection and radiation
Water does not always expand when heated
→ Thermal expansion of solids and liquids

Specific Heat, Latent Heat and Mixing

Formulas (3)

Specific heat capacity: the energy to warm a mass · Heating without a change of state $Q = m c \Delta T \qquad Q = P t$
Latent heat and changes of state · Energy for a change of state $Q = m L$
Calorimetry: heat lost equals heat gained · Mixing in an insulated container $m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2)$

Watch out for (5)

Power times time needs seconds
→ Specific heat capacity: the energy to warm a mass
Thermal conductivity is not specific heat capacity
→ Specific heat capacity: the energy to warm a mass
Melting breaks forces between molecules, not bonds inside them
→ Latent heat and changes of state
The temperature does not rise during a change of state
→ Latent heat and changes of state
Melted ice must still warm up
→ Calorimetry: heat lost equals heat gained

Ideal Gases and Kinetic Theory

Formulas (2)

The ideal gas equation and the three gas laws · Ideal gas equation $pV = nRT \qquad \frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$
Kinetic theory: temperature and molecular speed · Mean kinetic energy of a molecule $\overline{E_k} = \tfrac{1}{2} m \langle v^2 \rangle = \tfrac{3}{2} k_B T$

Watch out for (3)

Gas laws need kelvin, never Celsius
→ The ideal gas equation and the three gas laws
Boyle's law is not a straight line on a p against V graph
→ The ideal gas equation and the three gas laws
Heavier molecules do not have more kinetic energy
→ Kinetic theory: temperature and molecular speed

The First Law and Gas Processes

Formulas (1)

The first law of thermodynamics and the work done by a gas · First law and work at constant pressure $\Delta U = Q - W \qquad W = p\,\Delta V$

Reference tables (1)

Isothermal, isobaric, isochoric and adiabatic processes4 rows

Process	What stays constant	First law becomes	Line on a p against V graph
Isothermal	Temperature, so the internal energy of an ideal gas	$Q = W$	A hyperbola, $pV$ constant
Isobaric	Pressure	$Q = \Delta U + p\Delta V$	A horizontal line
Isochoric	Volume, so no work is done	$Q = \Delta U$	A vertical line
Adiabatic	No heat in or out	$\Delta U = -W$	A curve steeper than the isotherm through the same point

Watch out for (2)

Work done by the gas and work done on it have opposite signs
→ The first law of thermodynamics and the work done by a gas
Adiabatic does not mean constant temperature
→ Isothermal, isobaric, isochoric and adiabatic processes

The Second Law, Entropy and Heat Engines

Formulas (1)

Heat engines, efficiency and the Carnot limit · Efficiency and the Carnot limit $\eta = \frac{W}{Q_h} = 1 - \frac{Q_c}{Q_h} \qquad \eta_{\max} = 1 - \frac{T_c}{T_h}$

Reference tables (1)

The second law and entropy5 rows

Process	Entropy change	Why
Ice melting	Increases	An ordered crystal becomes a disordered liquid
Liquid evaporating	Increases	Molecules spread out into a much larger volume as gas
Friction slowing a sliding block	Increases	Ordered motion becomes random thermal motion
Heat flowing from hot to cold	Increases overall	The cold body gains more entropy than the hot body loses
Frictionless swing of a pendulum in a vacuum	Close to zero	No energy is turned into heat, so the motion is reversible

Watch out for (3)

The Carnot formula needs kelvin
→ Heat engines, efficiency and the Carnot limit
No real engine reaches the Carnot efficiency
→ Heat engines, efficiency and the Carnot limit
Entropy can fall locally
→ The second law and entropy

PYQ weightage by concept

12 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

Temperature, Heat and How Heat Moves0 PYQs · 0%

Concept	PYQs	Share
Temperature, heat and the Kelvin scalefoundation	—	—
Heat transfer: conduction, convection and radiationfoundation	—	—
Thermal expansion of solids and liquidsfoundation	—	—

Specific Heat, Latent Heat and Mixing0 PYQs · 0%

Concept	PYQs	Share
Specific heat capacity: the energy to warm a massfoundation	—	—
Latent heat and changes of statefoundation	—	—
Calorimetry: heat lost equals heat gainedfoundation	—	—

Ideal Gases and Kinetic Theory0 PYQs · 0%

Concept	PYQs	Share
The ideal gas equation and the three gas lawsfoundation	—	—
Kinetic theory: temperature and molecular speedfoundation	—	—

The First Law and Gas Processes0 PYQs · 0%

Concept	PYQs	Share
The first law of thermodynamics and the work done by a gasfoundation	—	—
Isothermal, isobaric, isochoric and adiabatic processesfoundation	—	—

The Second Law, Entropy and Heat Engines0 PYQs · 0%

Concept	PYQs	Share
Heat engines, efficiency and the Carnot limitfoundation	—	—
The second law and entropyfoundation	—	—