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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
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Curriculum Equation Key Gibbs Free Energy FormulaFast Exam Solution
ΔG = ΔH - TΔS | (ΔG < 0: تلقائي Spontaneous, ΔG > 0: غير تلقائي, ΔG = 0: اتزان)
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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
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, Ufinal − Uinitial
  • Positive when the temperature rises
W
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

SituationQWΔU
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 insulated0−+
  • 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 Qnet = Wnet

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

1
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).
2
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).
3
Heat Engines, Carnot Efficiency, and Entropy
  • A heat engine extracts heat QH from a hot reservoir, does useful mechanical work W,
  • and expels waste heat QC to a cold reservoir; the theoretical maximum Carnot efficiency is η = 1 - (TC / TH),
  • while the second law dictates that the total entropy of an isolated system always increases.
4
Atmospheric pressure
  • Pressure of the air, about 1.01 × 105 Pa at sea level.
5
Entropy
  • A measure of the number of possible arrangements of particles and energy, S = kB ln Ω.
6
Efficiency
  • Useful output divided by total input.
7
Reservoir
  • Artificial lake that stores water.
8
Adiabatic
  • With no thermal energy transfer
9
Isothermal
  • At constant temperature
10
Carnot cycle
  • A reversible cycle of two isothermal and two adiabatic processes between two reservoirs.
11
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)
12
Isolated system
  • System with no net external force.

Key terms

TermMeaning
First law of thermodynamicsThe 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 energyEnergy cannot be created or destroyed, only transferred or transformed.

Avoid these mistakes

1
Using the wrong sign for W — in Q = ΔU + W the work W is done by the gas.
2
Taking Q as positive when heat leaves the system — Q is negative for heat lost.
3
Forgetting ΔU = 0 over a whole cycle — the system returns to its initial state.
4
Saying a gas cannot change temperature without heat supplied — compression does work on the gas and can heat it with no heat transfer.
5
Using ΔU = (3/2)nRΔT for all substances — it holds only for ideal monatomic gases.

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