Sure!
Here's a simpler explanation:
Hydrostatic Pressure
The formula is:
P=ρghP = \rho g h
● What it means: This calculates the pressure a liquid creates at a certain depth.
● Why it happens: The deeper you go, the more weight of the liquid is pressing down
on you.
What the terms mean:
1. PP: Pressure (how much force is pressing on an area).
2. ρ\rho: The fluid’s density (how heavy the liquid is for its size).
3. gg: Gravity (makes the liquid push down, about 9.8 m/s29.8 \, \text{m/s}^2 on Earth).
4. hh: Depth (how far below the surface you are).
Key idea:
● Pressure increases as you go deeper (hh).
● Heavier (denser) liquids like oil or mercury cause more pressure at the same depth.
Example:
If you're 10 m underwater in a swimming pool, and the water's density is 1000 kg/m31000 \,
\text{kg/m}^3:
P=1000⋅9.8⋅10=98,000 Pa (98 kPa).P = 1000 \cdot 9.8 \cdot 10 = 98,000 \, \text{Pa} \,
\text{(98 kPa)}.
This means the water pressure at 10 m is 98,000 Pascals (or 98 kPa).
Let me know if you'd like more examples!
Boyle's Law Simplified
Boyle's Law describes how the pressure and volume of a gas are related when the
temperature is constant.
The Formula:
P1V1=P2V2P_1 V_1 = P_2 V_2
● P1,V1P_1, V_1: The initial pressure and volume.
● P2,V2P_2, V_2: The pressure and volume after a change.
Key Idea:
● If you squeeze a gas into a smaller space (reduce volume), its pressure increases.
● If you let the gas expand (increase volume), its pressure decreases.
Why?
Gas particles are constantly moving and colliding with the walls of their container:
● Smaller volume: Particles hit the walls more often → higher pressure.
● Larger volume: Particles have more space → lower pressure.
Real-Life Example:
1. Syringe:
○ Pull the plunger out → the volume increases, and the pressure inside drops
(suction).
○ Push the plunger in → the volume decreases, and the pressure increases.
2. Diving:
○ As a scuba diver goes deeper, the pressure increases, and the gas in their
tank compresses.
Quick Summary:
Pressure and volume are inversely related:
● ↑Volume\uparrow \text{Volume}, ↓Pressure\downarrow \text{Pressure}.
● ↓Volume\downarrow \text{Volume}, ↑Pressure\uparrow \text{Pressure}.
As long as the temperature doesn't change.
Pressure-Temperature Relationship (Gay-Lussac's Law)
The formula:
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}
What It Means:
This law describes how the pressure of a gas changes when its temperature changes, as
long as the volume stays the same.
Key Idea:
● When you heat a gas, its particles move faster and collide with the walls more, so
the pressure increases.
● When you cool a gas, the particles move slower, and the pressure decreases.
Terms:
● P1,T1P_1, T_1: Initial pressure and temperature.
● P2,T2P_2, T_2: Final pressure and temperature.
Important: The temperature must be in Kelvin (K), not Celsius.
To convert:
TK=T°C+273T_{\text{K}} = T_{\text{°C}} + 273
Example:
If a gas has a pressure of 100 kPa100 \, \text{kPa} at 300 K300 \, \text{K}, and the
temperature rises to 600 K600 \, \text{K}, what’s the new pressure?
Solution:
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2} 100300=P2600\frac{100}{300} =
\frac{P_2}{600} P2=100⋅600300=200 kPaP_2 = \frac{100 \cdot 600}{300} = 200 \, \text{kPa}
So, the pressure doubles when the temperature doubles.
Quick Summary:
● Hotter gas → More pressure.
● Colder gas → Less pressure.
Only true if the gas is kept in the same space (constant volume).
SI UNITS:
Here’s a detailed list of all pressure-related formulas in physics, grouped by concepts:
1. Basic Pressure
P=FAP = \frac{F}{A}
● PP: Pressure (Pa\text{Pa}).
● FF: Force (N\text{N}).
● AA: Area (m2\text{m}^2).
2. Hydrostatic Pressure
P=ρghP = \rho g h
● PP: Pressure due to a fluid (Pa\text{Pa}).
● ρ\rho: Density of the fluid (kg/m3\text{kg/m}^3).
● gg: Acceleration due to gravity (9.8 m/s29.8 \, \text{m/s}^2).
● hh: Depth of the fluid (m\text{m}).
3. Atmospheric Pressure
P=P0+ρghP = P_0 + \rho g h
● P0P_0: Atmospheric pressure at the surface (≈101325 Pa\approx 101325 \,
\text{Pa}).
● Additional terms are the same as hydrostatic pressure.
4. Ideal Gas Law (Pressure-Volume-Temperature Relationship)
PV=nRTP V = n R T
● PP: Pressure (Pa\text{Pa}).
● VV: Volume (m3\text{m}^3).
● nn: Amount of gas (mol\text{mol}).
● RR: Universal gas constant (8.314 J/mol\cdotpK8.314 \, \text{J/mol·K}).
● TT: Temperature (K\text{K}).
5. Boyle's Law (Pressure-Volume Relationship)
P1V1=P2V2P_1 V_1 = P_2 V_2
● For a gas at constant temperature, pressure and volume are inversely related.
6. Gay-Lussac's Law (Pressure-Temperature Relationship)
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}
● Pressure is directly proportional to absolute temperature, provided volume is
constant.
7. Bulk Modulus and Pressure
B=−ΔPΔVVB = -\frac{\Delta P}{\frac{\Delta V}{V}}
● BB: Bulk modulus (Pa\text{Pa}).
● ΔP\Delta P: Change in pressure (Pa\text{Pa}).
● ΔVV\frac{\Delta V}{V}: Relative change in volume.
8. Pascal’s Principle
ΔP=ρgΔh\Delta P = \rho g \Delta h
● Change in pressure is proportional to the change in height in a fluid.
9. Pressure in Fluids with Surface Tension
P=2γrP = \frac{2 \gamma}{r}
● γ\gamma: Surface tension (N/m\text{N/m}).
● rr: Radius of curvature of the surface (m\text{m}).
10. Bernoulli’s Equation
P+12ρv2+ρgh=constantP + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}
● Combines pressure, kinetic energy per unit volume, and potential energy per unit
volume in a fluid.
11. Vapour Pressure
Pvapour=Pexternal−ΔPboilingP_{\text{vapour}} = P_{\text{external}} - \Delta
P_{\text{boiling}}
● Related to phase changes and boiling point adjustments.
12. Tire Pressure (Gauge Pressure)
Pabsolute=Pgauge+PatmosphericP_{\text{absolute}} = P_{\text{gauge}} +
P_{\text{atmospheric}}
● Converts gauge pressure (measured above atmospheric pressure) to absolute
pressure.
13. Osmotic Pressure
Π=iMRT\Pi = i M R T
● Π\Pi: Osmotic pressure (Pa\text{Pa}).
● ii: Van 't Hoff factor.
● MM: Molarity (mol/L\text{mol/L}).
● RR: Gas constant (8.314 J/mol\cdotpK8.314 \, \text{J/mol·K}).
● TT: Temperature (K\text{K}).
If you need a deeper explanation of any specific formula or its use case, let me know!
