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.4.2 First Law of Thermodynamics — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 34 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.4.2 First Law of Thermodynamics — IB PHYSICS HL notes: State the first law as Q = ΔU + W, apply its sign convention and use it to analyse changes in a gas.Basis — the first law is conservation of energy applied to heat, work and internal energyWords — energy supplied by heating…

Alternative convention
Internal energy of a monatomic ideal gas
Complete cycle
Constant pressure
Compression
Constant volume

Part 1 of 8Statement of the first law

1Basis

Basis the first law is conservation of energy applied to heat, work and internal energy

2Words

Words energy supplied by heating = change in internal energy + work done by the system

3Equation

Q = ΔU + W
It can be rearranged to ΔU = Q − W

4Scope

Scope it applies to every process, reversible or not, and to all systems, not only gases

Part 2 of 8Meaning of the symbols and signs

Q energy supplied to the system by heating in J

Positive when heat flows in and negative when heat flows out

ΔU

ΔU change in internal energy, U_final − U_initial
Positive when the temperature rises

W work done by the system on the surroundings

Positive for expansion and negative for compression

Alternative convention

Alternative convention some books use a different sign for W, so always state the convention in use

Part 3 of 8Interpreting the signs

Situation	Q	W	ΔU
Gas heated and expands	+	+	depends on the balance
Gas compressed and heat lost	−	−	depends on the balance
Rigid container heated	+	0	+
Gas compressed quickly and insulated	0	−	+

Last row
- a bicycle pump warms because work done on the air raises its internal energy without any heat input

Part 4 of 8Calculating each term

1Work

W = pΔV at constant pressure, or the area under the p–V curve

2Internal energy of a monatomic ideal gas

ΔU = (3/2)nRΔT = (3/2)Δ(pV)

3Heat

Heat given directly, or found from Q = ΔU + W
For substances it can also be Q = mcΔT or Q = mL

4Complete cycle

Complete cycle the system returns to its initial state so ΔU = 0 and Q_net = W_net

Part 5 of 8Constant pressure and constant volume graphs

Constant pressure

Constant pressure a horizontal line on a p–V graph
Work is the area under the line

Expansion

Expansion the volume increases and work is done by the gas on its surroundings

Compression

Compression the volume decreases and work is done on the gas, so the internal energy rises if no heat escapes

Constant volume

Constant volume a vertical line with zero area
No work is done when the volume stays the same

Part 6 of 8Energy transfer at molecular level

Heating

Heating faster molecules in the surroundings collide with the slower molecules in the walls and give them kinetic energy

Expansion

Expansion molecules rebound from the retreating piston with less speed, so the gas loses kinetic energy as work is done by the gas

Compression

Compression molecules rebound from the approaching piston faster, so the gas gains kinetic energy as work is done on the gas

Result

Result a gas cools when it expands and warms when it is compressed unless heat flow compensates

Part 7 of 8Limits of the first law

1Direction

Direction the first law says energy is conserved but not whether a process can happen
Heat flowing from cold to hot would obey it yet never occurs

2Ideal gas assumption

Ideal gas assumption it is used only to find ΔU from the temperature change

3Further law

Further law the direction of change is decided by the second law

Part 8 of 8More from the specification

First Law of Thermodynamics

The first law of thermodynamics states that the change in internal energy ΔU of a system of particles equals the thermal energy Q transferred into the system minus the work done W by the system (ΔU = Q - W).

Thermodynamic Processes (Isothermal and Adiabatic)

In an isothermal expansion at constant temperature, ΔU = 0 so work done is equal to heat supplied (Q = W);
- in a rapid adiabatic expansion where Q = 0, work done by the gas reduces its internal energy (ΔU = -W).

Heat Engines, Carnot Efficiency, and Entropy

A heat engine extracts heat Q_H from a hot reservoir, does useful mechanical work W,
and expels waste heat Q_C to a cold reservoir; the theoretical maximum Carnot efficiency is η = 1 - (T_C / T_H),
while the second law dictates that the total entropy of an isolated system always increases.

Atmospheric pressure

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

Entropy

A measure of the number of possible arrangements of particles and energy, S = kB ln Ω.

Efficiency

Useful output divided by total input.

Reservoir

Artificial lake that stores water.

Adiabatic

With no thermal energy transfer

Isothermal

At constant temperature

Carnot cycle

A reversible cycle of two isothermal and two adiabatic processes between two reservoirs.

Energy transferred

W = V Q, in joules.
What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)

Isolated system

System with no net external force.

Key terms

Term	Meaning
First law of thermodynamics	The heat supplied to a system equals the increase in its internal energy plus the work done by the system, Q = ΔU + W.
Heat (Q)	Energy transferred because of a temperature difference.
Work (W)	Energy transferred by a force moving through a distance; for a gas W = pΔV.
Change in internal energy (ΔU)	The change in the total molecular kinetic and potential energy.
Conservation of energy	Energy cannot be created or destroyed, only transferred or transformed.

Avoid these mistakes

Using the wrong sign for W — in Q = ΔU + W the work W is done by the gas.

Taking Q as positive when heat leaves the system — Q is negative for heat lost.

Forgetting ΔU = 0 over a whole cycle — the system returns to its initial state.

Saying a gas cannot change temperature without heat supplied — compression does work on the gas and can heat it with no heat transfer.

Using ΔU = (3/2)nRΔT for all substances — it holds only for ideal monatomic gases.

Last updated: 15 October 2026