• 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?by?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?on?a gas)

• 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

Positive or negative work done depends on whether the gas is compressed or expanded

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

Work is only done when the volume of a gas changes

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.)