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:
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
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.)