The First Law Of Thermodynamics (Copy)

Introduction

• The first law of thermodynamics is a statement of the conservation of energy applied to thermal systems.
• It connects internal energy (U), heat (q), and work (W).
• It describes how energy is transferred to or from a system and how it affects the system’s internal energy.

The First Law of Thermodynamics

∆U = q + W

Where:
∆U = change in internal energy (J)
q = heat supplied to the system (J)
W = work done on the system (J)

• All terms are in joules (J)
• This form of the law uses sign conventions where:
  • q > 0 when heat is added to the system
  • W > 0 when work is done on the system
  • ∆U > 0 when internal energy increases

Alternative Sign Convention (Physics)

In some textbooks and exam questions (including A Level Physics), you may also see:

∆U = q – W’

Where:
W’ = work done by the system (e.g. gas expanding against external pressure)

So, depending on the convention used:

In this topic, we use Physics convention:

• Work on the gas is positive
• Work by the gas is negative

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

1. Work Done by a Gas at Constant Pressure

When the volume of a gas changes at constant pressure:

W = p∆V

Where:
W = work done on the gas (J)
p = pressure of the gas (Pa)
∆V = change in volume = final volume – initial volume (m³)

Interpretation:

• If ∆V > 0 (expansion), the gas does work on the surroundings ⇒ W is negative
• If ∆V < 0 (compression), surroundings do work on the gas ⇒ W is positive

Units:

• p in pascals (Pa = N/m²)
• V in cubic metres (m³)
• So p∆V has units:
  Pa × m³ = N/m² × m³ = Nm = Joules (J)

Real-Life Analogy

• Imagine a gas in a piston:
  • If the gas expands, it pushes the piston outward → does work on the piston
  • If the piston compresses the gas, work is done on the gas → internal energy increases

2. Full Statement of the First Law (Physics Convention)

∆U = q + W

Where:

• ∆U: change in internal energy
• q: thermal energy supplied to system
• W: work done on the system

Breakdown of Terms

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Examples

Example 1: Work done on a gas
A gas is compressed from 0.040 m³ to 0.030 m³ at a pressure of 1.2 × 10⁵ Pa. Calculate the work done on the gas.

∆V = V_final – V_initial = 0.030 – 0.040 = –0.010 m³
W = p∆V = (1.2 × 10⁵) × (–0.010) = –1200 J

Since the gas was compressed, work is done on the gas:
W = +1200 J

Example 2: Internal energy change
A gas receives 500 J of heat and expands, doing 200 J of work on the surroundings. Find ∆U.

W (on gas) = –200 J
q = +500 J
∆U = q + W = 500 + (–200) = +300 J

Internal energy increases by 300 J

Conservation of Energy

• The first law is ultimately a conservation of energy principle:
  • Energy supplied to the system (by heating and doing work) goes into increasing its internal energy.
• Energy cannot be created or destroyed, only converted between heat, work, and internal energy.

Energy Flow Diagram

      HEAT (q)
        ↓
  ----------------
 |   SYSTEM       | → WORK DONE (W)
 |  ∆U increases  |
  ----------------

Summary Table

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course