Thermodynamics - a MaS Tutor.

Specific Heat Capacity

Δ E = m c Δ θ

where $Δ E$ is the change in internal energy (J);
$m$ is the mass of the material (kg);
$c$ is the specific heat capacity (Jkg^-1K^-1);
$Δ θ$ is the change in temperature (K).

Gas Laws

Boyle's_law

p V = constant

at constant temperature (isothermal)

Charles' Law

\frac{V}{T} = constant

at constant pressure (isobaric)

Gay-Lussac's law
(AKA The Pressure Law)

\frac{p}{T} = constant

at constant volume (isochoric)

$p$ is the gas pressue (Pa);
$V$ is the volume of the gas (m³);
$T$ is the temperature of the gas (K).

Ideal Gas Law

p V = n R T

p V = N k T

\Rightarrow n R = N k

If $N = N_{A}$ then $n = 1$ , so

k = \frac{R}{N_{A}}

Gas Constant $R = 8.31 J K^{–1} {mol}^{–1}$

Density form of the ideal gas equation

p = \frac{1}{3} ρ {(c_{RMS})}^{2}