First Law of Thermodynamics (DP IB Physics) : Revision Note

Katie M

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Katie M

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The First Law of Thermodynamics

  • The first law of thermodynamics is based on the principle of conservation of energy

  • When energy is put into a gas by heating it or doing work on it, its internal energy must increase:

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

  • The first law of thermodynamics is therefore defined as:

Q space equals space increment U space plus thin space W

  • Where:

    • Q = energy supplied to the system by heating (J)

    • ΔU = change in internal energy (J)

    • W = work done by the system (J)

  • The first law of thermodynamics applies to all situations, not just to gases

    • There is an important sign convention used for this equation

  • A positive value for internal energy (+ΔU) means:

    • The internal energy ΔU increases

    • Heat Q is added to the system (+Q)

    • Work W is done on the system (–W)

  • A negative value for internal energy (−ΔU) means:

    • The internal energy ΔU decreases

    • Heat Q is taken away from the system (–Q)

    • Work W is done by the system (+W)

Graphs of Constant Pressure & Volume

  • Graphs of pressure p against volume V can provide information about the work done and internal energy of the gas

    • The work done is represented by the area under the line

  • A constant pressure process is represented as a horizontal line

    • If the volume is increasing (expansion), work is done by the gas (on the surroundings) and internal energy decreases (ΔqW)

    • If the arrow is reversed and the volume is decreasing (compression), work is done on the gas and internal energy increases (ΔqW)

    • The volume of the gas is made smaller, so more collisions between the molecules of the gas and the walls of the container occur. This creates a higher pressure. 

  • A constant volume process is represented as a vertical line

    • In a process with constant volume, the area under the curve is zero

    • Therefore, no work is done when the volume stays the same

Work is only done when the volume of a gas changes

Worked Example

The volume occupied by 1.00 mol of a liquid at 50°C is 2.4 × 10−5 m3. When the liquid is vaporised at an atmospheric pressure of 1.03 × 105 Pa, the vapour occupies a volume of 5.9 × 10−2 m3.

The latent heat to vaporise 1.00 mol of this liquid at 50°C at atmospheric pressure is 3.48 × 104 J.

For this change of state, determine the increase in internal energy ΔU of the system.

Answer:

Step 1: List the known quantities

  • Thermal energy, Q = 3.48 × 104 J

  • Atmospheric pressure, p = 1.03 × 105 Pa

  • Initial volume = 2.4 × 10−5 m3

  • Final volume = 5.9 × 10−2 m3

Step 2: Calculate the work done W

  • The work done by a gas at constant pressure is

W space equals space p increment V

  • Where the change in volume is: 

ΔV = final volume − initial volume = (5.9 × 10−2) − (2.4 × 10−5) = 0.059 m3

  • Since the volume of the gas increases, the work done is positive

W = (1.03 × 105) × 0.059 = 6077 = 6.08 × 103 J

W = +6.08 × 103 J

Step 3: Substitute the values into the equation for the first law of thermodynamics

  • From the first law of thermodynamics:

increment U space equals space Q thin space minus thin space W

ΔU = (3.48 × 104) − (6.08 × 103) = 28 720 J

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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