Laws of Thermodynamics: MDCAT Chemistry notes
Laws of Thermodynamics MDCAT notes: first law, sign conventions, pressure-volume work, constant volume and pressure, bomb calorimeter.
First law of thermodynamics
Energy can neither be created nor destroyed, but can be converted from one form to another. The total energy of a system and its surroundings remains constant.
Mathematically:
$$\Delta E = q + w$$
- $\Delta E$: change in internal energy of the system.
- $q$: heat absorbed by the system (positive) or released (negative).
- $w$: work done on the system (positive) or by the system (negative).
Pressure-volume work
When a gas expands or contracts against a constant external pressure:
$$w = -P\Delta V = -P(V_2 - V_1)$$
- Expansion ($\Delta V \gt 0$): the system does work, so $w$ is negative.
- Compression ($\Delta V \lt 0$): work is done on the system, so $w$ is positive.
- If a reaction changes the number of moles of gas, the volume of the system changes and work is done.
- $1\ \mathrm{dm^3\,atm} = 101.3\ \mathrm{J}$.
Worked example
A gas expands from $10\ \mathrm{dm^3}$ to $16\ \mathrm{dm^3}$ against a constant 3 atm. $w = -3\times6 = -18\ \mathrm{dm^3\,atm} = -18\times101.3 \approx -1823\ \mathrm{J}$. The negative sign shows the gas did work on the surroundings.
Gas-evolving reactions
When a reaction gives off a gas, for example a carbonate or a metal reacting with dilute acid, the gas pushes back the atmosphere. The system does work on the surroundings, so $w$ is negative. The sign of $q$ depends on whether that particular reaction releases or absorbs heat.
Applications of the first law
| Condition | Result | Meaning |
|---|---|---|
| Constant volume ($\Delta V = 0$) | $w = 0$, so $\Delta E = q_v$ | Heat supplied equals the change in internal energy |
| Constant pressure | $q_p = \Delta E + P\Delta V = \Delta H$ | Heat supplied equals the enthalpy change |
| Isolated system | $q = 0$, $w = 0$, so $\Delta E = 0$ | Energy is conserved |
A bomb calorimeter is a sealed, rigid steel vessel. Its volume is constant, so it measures $\Delta E$. A coffee-cup (glass) calorimeter works at constant pressure and measures $\Delta H$.
Hess's law is an application of the first law: since energy is conserved and $H$ is a state function, the enthalpy change is the same by any route.
Second law (brief)
The first law tells us energy is conserved but not which direction a change will go. The second law states that in a spontaneous process the total entropy (disorder) of the system and surroundings increases. Heat flows naturally from a hot body to a cold one, never the reverse on its own.
Key formulas
- $\Delta E = q + w$
- $w = -P\Delta V$
- $\Delta E = q_v$ and $\Delta H = q_p = \Delta E + P\Delta V$
Common MDCAT traps
- The correct form of the first law is $\Delta E = q + w$, not $\Delta E = w - q$ or $\Delta H = q + w$.
- In expansion work is done by the gas, so $w$ is negative.
- At constant volume the heat equals $\Delta E$, not $\Delta H$.
- A bomb calorimeter keeps volume constant, not pressure.
- Keep units consistent: $\mathrm{dm^3\,atm}$ must be converted to J before adding to $q$.
Quick revision
- First law: energy is conserved.
- $\Delta E = q + w$.
- Expansion work is negative.
- Bomb calorimeter works at constant volume.
- Hess's law follows from the first law.