• 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:

The increase in internal energy = Energy supplied by heating + Work done on the system

• The first law of thermodynamics is therefore defined as:

ΔU = q + W

• Where:
  • ΔU = increase in internal energy (J)
  • q = energy supplied to the system by heating (J)
  • W = work done on the system (J)

• The first law of thermodynamics applies to all situations, not just for 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
  • Work W is done on the system (or on a gas)
• A negative value for internal energy (−ΔU) means:
  • The internal energy ΔU decreases
  • Heat q is taken away from the system
  • Work W is done by the system (or by a gas) on the surroundings

• This is important when thinking about the expansion or compression of a gas
• When the gas expands, it transfers some energy (does work) to its surroundings
• This decreases the overall energy of the gas
• Therefore, when the gas expands, work is done by the gas (−W)

When a gas expands, work done W is negative

• When the gas is compressed, work is done on the gas (+W)

When a gas is compressed, work done W is positive

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

Worked example

Step 1:

Write down the first law of thermodynamics

ΔU = q + 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 = pΔV

ΔV = final volume − initial volume = 5.9 × 10^-2 − 2.4 × 10^-5 = 0.058976 m³

p = atmospheric pressure  = 1.03 × 10⁵ Pa

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

Since the gas is expanding, this work done is negative

W = −6.07 × 10³ J

Step 4:

Substitute the values into first law of thermodynamics

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