Last-night recap — not a substitute for the lessons.
| Quantity | Equation | Units |
|---|---|---|
| Density | $\rho=m/V$ | kg/m³, kg, m³ |
| Pressure | $p=F/A$ | Pa $=\text{N/m}^2$ |
| Fluid pressure difference | $p=h\rho g$ | m, kg/m³, N/kg $\rightarrow$ Pa |
| Boyle (constant $T$) | $p_1V_1=p_2V_2$ | any consistent $p$, $V$ |
| Pressure law (constant $V$) | $p_1/T_1=p_2/T_2$ | $T$ in kelvin only |
| Kelvin | $T=\theta+273$ | K, °C |
$g=10\,\text{N/kg}$. Water $\rho\approx 1000\,\text{kg/m}^3$. Atmosphere often $1.00\times 10^5\,\text{Pa}$ if given.
Regular solid
Balance for $m$. Ruler or callipers for $l,w,h$. $V=lwh$ or $\pi r^2 h$. Repeats.
Liquid
Mass of empty cylinder, pour liquid, meniscus at eye level, $m$ by difference, $V$ from the scale.
Irregular / eureka
Mass dry. Fill can to spout. Collect overflow $=$ $V$. Sinker if it floats. Watch bubbles and drops.
| Change | Constant | Equation | Particle sentence |
|---|---|---|---|
| $V$ down | $T$, mass | $p_1V_1=p_2V_2$ | More frequent collisions (speed unchanged) |
| $T$ up | $V$, mass | $p_1/T_1=p_2/T_2$ | Faster / harder and more frequent collisions |
Absolute zero $-273^\circ\text{C}=0\,\text{K}$. $T\propto$ average KE. Gas pressure $=$ collisions with walls.