Key Equations
Thermal Physics - OCR A-Level Physics
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Energy for temperature change
$$Q = mc\Delta\theta$$
- Where:
- $Q$ = J
- $m$ = kg
- $c$ = J kg^{-1} \(K^{-1}\)
- $\Delta\theta$ = K or \degree C
Use when a substance changes temperature without changing state.
Energy for change of state
$$Q = mL$$
- Where:
- $Q$ = J
- $m$ = kg
- $L$ = J kg^{-1}
Use when a substance changes state at constant temperature.
Ideal gas equation (moles)
$$pV = nRT$$
- Where:
- $p$ = Pa
- $V$ = \(m^{3}\)
- $n$ = mol
- $R$ = 8.31 J mol^{-1} \(K^{-1}\)
- $T$ = K
Use when working with moles of gas. T must be in Kelvin.
Ideal gas equation (molecules)
$$pV = NkT$$
- Where:
- $p$ = Pa
- $V$ = \(m^{3}\)
- $N$ = number of molecules
- $k$ = 1.38 \times \(10^{-23}\) J \(K^{-1}\)
- $T$ = K
Use when working with number of molecules. T must be in Kelvin.
Mean kinetic energy of a molecule
$$\frac{1}{2}m\langle c^2 \rangle = \frac{3}{2}kT$$
- Where:
- $m$ = kg (mass of one molecule)
- $\langle c^2 \rangle$ = \(m^{2}\) \(s^{-2}\)
- $k$ = J \(K^{-1}\)
- $T$ = K
Links molecular KE to temperature. Average KE is the same for all ideal gas molecules at the same temperature regardless of mass.
Kinetic theory equation
$$pV = \frac{1}{3}Nm\langle c^2 \rangle$$
- Where:
- $p$ = Pa
- $V$ = \(m^{3}\)
- $N$ = number of molecules
- $m$ = kg
- $\langle c^2 \rangle$ = \(m^{2}\) \(s^{-2}\)
Derived from kinetic theory. Links macroscopic gas properties (p, V) to molecular motion. The 1/3 comes from averaging over 3 dimensions.
Kelvin-Celsius conversion
$$T(K) = T(\degree C) + 273$$
- Where:
- $T$ = K or \degree C
Must memorise. Always convert to Kelvin before using gas law or kinetic theory equations.
Boltzmann constant
$$k = \frac{R}{N_A}$$
- Where:
- $k$ = J \(K^{-1}\)
- $R$ = J mol^{-1} \(K^{-1}\)
- $N_A$ = mol^{-1}
Must memorise. Links the molar gas constant to the molecular Boltzmann constant.