A LevelPhysicsCambridge (CIE)Revision Notes16. ThermodynamicsThe First Law of ThermodynamicsThe First Law of Thermodynamics

The First Law of Thermodynamics (Cambridge (CIE) A Level Physics): Revision Note

Exam code: 9702

Ann Howell

Last updated

The first law of thermodynamics

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

  • When thermal energy is added to a gas by heating it or doing work on it, its internal energy must increase:

The increase in internal energy of a system is equal to the sum of the thermal energy added to the system and the work done on it

  • The first law of thermodynamics is therefore defined as:

increment U space equals space q space plus thin space W

  • Where:

    • ΔU = increase in internal energy (J)

    • q = thermal energy added to the system (J)

    • W = work done on the system (J)

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

    • There is an important sign convention used for this equation

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

    • The internal energy ΔU of the system increases

    • Heat (+q) is added to the system

    • Work (+W) is done on the system

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

    • The internal energy ΔU of the system decreases

    • Heat (-q) is taken away from the system

    • Work (-W) is done by the system

Worked Example

The volume occupied by 1.00 mol of a liquid at 50 oC is 2.4 × 10-5 m3. When the liquid is vaporised at an atmospheric pressure of 1.03 × 105 Pa, the vapour has a volume of 5.9 × 10-2 m3. The latent heat to vaporise 1.00 mol of this liquid at 50 oC at atmospheric pressure is 3.48 × 104 J.

Determine, for this change of state, the change in the internal energy of the system.

Answer: 

Step 1: Write down the first law of thermodynamics

increment U space equals space q thin space plus thin space W

Step 2: Write the value of heating q of the system

  • This is the latent heat, the heat required to vaporise the liquid = 3.48 × 104 J

Step 3: Calculate the work done W

W space equals space p increment V

  • ΔV = final volume − initial volume

ΔV = 5.9 × 10-2 − 2.4 × 10-5 = 0.058976 m3

  • p = atmospheric pressure  = 1.03 × 105 Pa

  • W = work done

W = (1.03 × 105) × 0.058976 = 6074.528 = 6.07 × 103 J

  • Since the gas is expanding, the work done is negative

W = −6.07 × 103 J

Step 4: Substitute the values into the first law of thermodynamics

ΔU = 3.48 × 104  + (−6.07 × 103) = 28 730 = 29 000 J (2 s.f.)

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    Ann Howell

    Author: Ann Howell

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    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.