Revise Thermal equilibrium for Cambridge 9702 (14.1)

Thermal equilibrium occurs when two or more objects in thermal contact reach the same temperature. At this point, there's no longer a net flow of thermal energy from one object to another. Energy might still be exchanged at a microscopic level, but on average, the rate of energy flowing in one direction equals the rate flowing in the opposite direction. This stable state means all parts of the system are at a uniform temperature.

This law might sound trivial, but it forms the foundation for temperature measurement. It states: If object A and object B are both in thermal equilibrium with a third object C, then objects A and B are also in thermal equilibrium with each other. Think of object C as a thermometer – if two objects give the same reading on a thermometer, they must be at the same temperature.

Temperature is a fundamental physical quantity that gives us a quantitative measure of how 'hot' or 'cold' something is. At a microscopic level, it's directly related to the average random kinetic energy of the particles (atoms or molecules) within a substance. The faster these particles vibrate or move, the higher the temperature.

While Celsius (°C) is common, the Kelvin (K) scale is the SI unit for absolute temperature and is used in almost all physics formulas. It's an absolute scale, meaning 0 K represents the lowest possible temperature, known as absolute zero. At absolute zero (-273.15 °C), particles possess the minimum possible kinetic energy. A change of 1 Kelvin is exactly equivalent to a change of 1 degree Celsius.

To convert Celsius to Kelvin: K = C + 273.15

The internal energy of a system is the total sum of the random kinetic and potential energies of all its particles. The kinetic energy component is due to the random motion of particles (translation, rotation, vibration) and is directly linked to temperature. The potential energy component arises from the intermolecular forces between particles. When a substance changes state, its potential energy changes significantly, even if its temperature (and thus average kinetic energy) remains constant.

When you add thermal energy to a substance, its temperature usually rises. Specific heat capacity (c) quantifies how much energy is needed to change the temperature of a unit mass of a substance by 1 Kelvin (or 1 °C) without a change of state. Substances with high specific heat capacity (like water) require a lot of energy to heat up, making them excellent coolants.

Energy transferred during temperature change: $Q = mc\Delta T$. Units for c: J kg⁻¹ K⁻¹

Sometimes, adding energy to a substance doesn't increase its temperature, but instead changes its state (e.g., melting ice into water or boiling water into steam). This energy is called latent heat. Specific latent heat (L) is the energy required to change the state of 1 kg of a substance without changing its temperature. The energy supplied goes into altering the potential energy of the particles by breaking or forming intermolecular bonds.

There are two main types:

Energy transferred during state change: Q = mL \ Units for L: J kg⁻¹

Evaporation is a fascinating example of a cooling process related to latent heat. When a liquid evaporates, higher-energy particles escape from the liquid surface. This reduces the average kinetic energy of the remaining particles in the liquid, leading to a decrease in the liquid's overall temperature.

The specific heat capacity and specific latent heat of substances can be determined experimentally, most commonly using an electrical method. For specific heat capacity, a known mass (m) of the substance is heated by an electrical heater of known power (P) for a measured time (t). The initial and final temperatures are recorded to find the change (ΔT). The energy supplied is E = Pt. By equating E = mcΔT, 'c' can be calculated. For specific latent heat, a similar setup is used, but the substance is held at its melting or boiling point. The energy (E = Pt) required to change the state of a measured mass (m) is recorded, and L is found using E = mL.

The primary source of error in these experiments is heat loss to the surroundings. This makes the calculated values of 'c' and 'L' higher than the true values, as not all the supplied electrical energy goes into heating the substance. To mitigate this:

• Use insulation (lagging) around the container.
• Place a lid on the container to reduce heat loss by convection and evaporation.
• Polish the outer surfaces to reduce heat loss by radiation.
• A more advanced technique is to start the experiment with the substance at a temperature below room temperature and end it at an equal temperature above room temperature, allowing heat lost in the second half to be roughly balanced by heat gained in the first half.