كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme B — The Particulate Nature of Matter

B.4 Thermodynamics — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 32 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

B.4 Thermodynamics — IB PHYSICS HL notes: Apply the first and second laws of thermodynamics to ideal gases, the four thermodynamic processes, entropy and heat-engine cycles.Internal energy of an ideal gas — all of it is random kinetic energy because ideal gas molecules have no in…

Work at constant pressure
Work when pressure changes
Sign convention
All processes
Pressure–volume relation
Temperature–volume relation

Part 1 of 8Internal energy and work done by a gas

Internal energy and work done by a gas

Internal energy of an ideal gas

Internal energy of an ideal gas all of it is random kinetic energy because ideal gas molecules have no intermolecular forces
ΔU = (3/2)NkBΔT = (3/2)nRΔT
ΔU is proportional to the change in thermodynamic temperature in kelvin

Work at constant pressure

W = pΔV
W is positive when the gas expands and negative when it is compressed
The pressure is that of the surroundings, which changes very slowly

Work when pressure changes

Work when pressure changes the work equals the area under the curve on a p–V diagram
No work is done when the volume is constant

Part 2 of 8First law of thermodynamics

1Statement

Statement energy supplied by heating = increase in internal energy + work done by the system
Q = ΔU + W, based on conservation of energy
It applies to every system, not only to gases

2Sign convention

Q is positive when heat enters the system and W is positive when the system does work
ΔU is positive when the internal energy rises

3Cycle

Cycle over a whole cycle ΔU = 0 so the net heat equals the net work

Part 3 of 8The four thermodynamic processes

Process	Fixed quantity	Result from Q = ΔU + W
Isovolumetric	V constant	W = 0 so Q = ΔU
Isobaric	p constant	W = pΔV so Q = ΔU + pΔV
Isothermal	T constant	ΔU = 0 so Q = W
Adiabatic	Q = 0	W = −ΔU, so the temperature changes

All processes
- the gas is assumed to be ideal

Part 4 of 8Adiabatic changes of a monatomic ideal gas

Adiabatic changes of a monatomic ideal gas

Pressure–volume relation

Pressure–volume relation pV^5/3 = constant
p₁V₁^5/3 = p₂V₂^5/3

Temperature–volume relation

TV^2/3 = constant, found by substituting p = nRT/V
T₁V₁^2/3 = T₂V₂^2/3

Curve shape

Curve shape an adiabatic curve on a p–V diagram is steeper than an isothermal curve through the same point

Part 5 of 8Entropy

Meaning

Meaning entropy is a measure of the number of possible arrangements of the particles and their energy
Entropy rises in the order solid, liquid, gas

Microscopic equation

S = kB ln Ω where Ω is the number of microstates
ΔS = kB ln(Ω₂/Ω₁)

Macroscopic equation

ΔS = Q/T at constant temperature
Heat gained gives ΔS > 0 and heat lost gives ΔS < 0

Part 6 of 8Second law of thermodynamics

1Entropy form

Entropy form the total entropy of an isolated system always increases
For a non-isolated system the entropy of the Universe must increase

2Clausius form

Clausius form thermal energy cannot spontaneously transfer from a colder region to a hotter region

3Kelvin form

Kelvin form it is impossible to convert all the energy extracted from a heat reservoir into work

4Reversible and irreversible

Reversible and irreversible a reversible process leaves the total entropy unchanged, a real (irreversible) process increases it

Part 7 of 8Heat engines and the Carnot cycle

1Heat engine

Heat engine a device that takes heat Q_H from a hot reservoir, does work and rejects Q_C to a cold reservoir
W_out = Q_H − Q_C equals the area of the p–V loop

2Efficiency

η = W_out/Q_H = 1 − Q_C/Q_H

3Carnot cycle

Carnot cycle the reversible cycle of isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression
Its efficiency is the maximum possible, η_C = 1 − T_C/T_H with temperatures in kelvin

Part 8 of 8More from the specification

Thermodynamics of a gas

Thermodynamics of a gas a piston compresses the gas so final volume is less than the initial volume

Work done by gas

W = P times change in volume at constant pressure, being the area under a P-V graph

Entropy

Entropy a measure of disorder, which decreases for a system when heat leaves it, though the total entropy of the universe does not decrease

Calculating changes

Calculating changes use first law, Q = change in U + W, and when volume decreases work is done on the gas

Piston

A moving part in a cylinder that applies or receives pressure.

Atmospheric pressure

Pressure of the air, about 1.01 × 10⁵ Pa at sea level.

Key terms

Term	Meaning
Isobaric	A process at constant pressure, W = pΔV.
Isovolumetric	A process at constant volume in which no work is done.
Isothermal	A process at constant temperature, so ΔU = 0 for an ideal gas.
Adiabatic	A process in which no heat enters or leaves the system, Q = 0.
Entropy	A measure of the number of possible arrangements of particles and energy, S = kB ln Ω.
Heat engine	A device that converts thermal energy into mechanical work using a closed cycle.
Carnot efficiency	The maximum efficiency of an engine between two reservoirs, 1 − T_C/T_H.

Avoid these mistakes

Taking the temperature change in °C as a ratio — internal energy is proportional to the change in kelvin, so heating from 50 °C to 150 °C does not triple it.

Saying an adiabatic change has no temperature change — Q = 0 but the work done changes the internal energy so the temperature changes.

Using the Carnot formula with Celsius temperatures — T_C and T_H must be in kelvin.

Claiming a heat engine can convert all input heat to work — some heat must always be rejected to the cold reservoir.

Last updated: 15 October 2026