← Theme B · Particulate Nature of Matter
Physics · Topic Cheatsheet

Theme B · Particulate Nature of Matter

35 key results accumulated across 3 chapters.

Temperature (kelvin)
Ch 1
TK=TC+273T_K = T_C + 273
Absolute zero = 0 K; molecular KE →\to 0.
Three transfer modes
Ch 1
Conduction (solids), convection (fluids), radiation (EM waves, works in vacuum).
Specific heat capacity
Ch 1
Q=mc ΔTQ = mc\,\Delta T
Latent heat (phase change)
Ch 1
Q=mLQ = mL
Temperature stays constant during melting/boiling.
Internal energy
Ch 1
Sum of random KE + PE of particles. For an ideal gas U∝TU \propto T.
Ideal gas law
Ch 1
pV=nRTpV = nRT
TT in kelvin; R=8.31R = 8.31 J mol⁻¹ K⁻¹.
Boyle's law (const T)
Ch 1
pV=const  ⇒  p1V1=p2V2pV = \text{const} \;\Rightarrow\; p_1V_1 = p_2V_2
Charles' law (const p)
Ch 1
VT=const\frac{V}{T} = \text{const}
Gay-Lussac (const V)
Ch 1
pT=const\frac{p}{T} = \text{const}
Kinetic theory
Ch 1
Pressure arises from particle collisions with walls; faster (hotter) ⇒ higher pressure.
Combined gas law
Ch 1
p1V1T1=p2V2T2\frac{p_1V_1}{T_1} = \frac{p_2V_2}{T_2}
Use when p, V and T all change. TT MUST be in kelvin.
Mean KE of a molecule
Ch 1
Eˉk=32kBT\bar{E}_k = \tfrac{3}{2}k_BT
kB=1.38×10−23k_B = 1.38\times10^{-23} J K⁻¹; depends only on T.
Pressure
Ch 1
p=FAp = \frac{F}{A}
Pa = N m⁻². In a liquid: p=ρghp=\rho g h (depth only).
Density & upthrust
Ch 1
ρ=mV\rho=\frac{m}{V}
Floats when upthrust = weight (Archimedes: upthrust = weight of fluid displaced).
Stefan–Boltzmann (radiation)
Ch 1
P=eσAT4P = e\sigma A T^4
Power ∝ T4T^4: double T ⇒ ×16 power.
Key SI units
Ch 1
TT: K · QQ: J · cc: J kg⁻¹ K⁻¹ · LL: J kg⁻¹ · pp: Pa · VV: m³ · nn: mol · ρ\rho: kg m⁻³.
Common traps
Ch 1
Using °C instead of K in gas laws; forgetting T is constant during a phase change; not converting cm³→m³ or g→kg.
Electric current
Ch 2
I=Qt  ⇔  Q=ItI = \frac{Q}{t}\;\Leftrightarrow\; Q = It
Rate of charge flow; amperes (A).
Voltage = energy/charge
Ch 2
V=WQ  ⇒  W=QV=VItV = \frac{W}{Q}\;\Rightarrow\; W = QV = VIt
Energy delivered; also W=PtW = Pt.
Ohm's law
Ch 2
V=IR    (R=V/I)V = IR\;\;(R = V/I)
Electrical power
Ch 2
P=VI=I2R=V2RP = VI = I^2R = \frac{V^2}{R}
Resistors in series
Ch 2
RT=R1+R2+⋯R_T = R_1 + R_2 + \cdots
Current SAME in each; voltages add (Vi=IRiV_i = IR_i).
Resistors in parallel
Ch 2
1RT=1R1+1R2+⋯\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots
Voltage SAME across each; currents add. Two: RT=R1R2R1+R2R_T=\tfrac{R_1R_2}{R_1+R_2}.
EMF & internal resistance
Ch 2
ε=I(R+r)\varepsilon = I(R + r)
Terminal voltage V=ε−IrV = \varepsilon - Ir.
1st law of thermodynamics
Ch 2
Q=ΔU+WQ = \Delta U + W
Energy conservation for a gas.
2nd law (entropy)
Ch 2
Total entropy never decreases; heat flows hot → cold spontaneously.
Carnot efficiency
Ch 2
ηmax⁡=1−TcoldThot\eta_{\max} = 1 - \frac{T_{cold}}{T_{hot}}
Temperatures in kelvin; no engine can beat this.
Charge & the coulomb
Ch 2
Q=ItQ = It
1 C = 1 A·s (charge when 1 A flows for 1 s). Electron charge e=1.6×10−19e = 1.6\times10^{-19} C.
Current direction
Ch 2
Conventional current: + → − in the external circuit. Real electrons flow the OPPOSITE way (− → +).
Inside a battery
Ch 2
Chemical energy does work to separate charge, maintaining the e.m.f. (energy per coulomb, V = J/C).
Battery symbol
Ch 2
Long thin bar = + terminal; short thick bar = − terminal.
Kirchhoff's laws
Ch 2
Junction: currents in = currents out. Loop: sum of e.m.f. = sum of IRIR drops (energy conservation).
Series vs parallel (why)
Ch 2
Series: same I, voltages add ⇒ R adds. Parallel: same V, currents add ⇒ total R < smallest branch.
Key SI units
Ch 2
II: A · QQ: C · VV, e.m.f.: V (= J C⁻¹) · RR: Ω · PP: W · WW: J.
Common traps
Ch 2
Confusing conventional current with electron flow; using kJ not J; forgetting internal resistance rr drops the terminal voltage.