Internal Energy

Specific Heat Capacity (SHC)

• SHC is the energy required to raise the temperature of $1$ kg of a substance by $1$ °C. It is used when a substance is being heated or cooled within a single state (solid, liquid, or gas).
• The formula is given by: $\Delta E = mc\Delta\theta$
• Where $\Delta E$ is the change in thermal energy (J), $m$ is the mass (kg), $c$ is the specific heat capacity (J/kg °C), and $\Delta\theta$ is the change in temperature (°C).

Specific Latent Heat (SLH)

• SLH is the energy required to change the state of $1$ kg of a substance without any change in temperature. It is used during melting, freezing, boiling, or condensing.
• The formula is given by: $E = mL$
• Where $E$ is the energy for state change (J), $m$ is the mass (kg), and $L$ is the specific latent heat (J/kg). There are two types: Latent Heat of Fusion (solid/liquid) and Latent Heat of Vaporization (liquid/gas).

• It is vital to distinguish between energy used for temperature change and energy used for state change. The following table summarizes the differences:

• Fusion vs. Vaporization: The latent heat of fusion applies to the transition between solid and liquid (melting/freezing), while the latent heat of vaporization applies to the transition between liquid and gas (boiling/condensing). Generally, vaporization requires significantly more energy than fusion for the same substance.

• Identify the Process: Always check if the question describes a temperature change or a state change. If the temperature is changing, use $mc\Delta\theta$; if the temperature is constant during heating, use $mL$.

• Unit Consistency: Ensure mass is in kilograms (kg). If a question provides mass in grams, divide by $1000$ before substituting into formulas to avoid magnitude errors.

• Graph Interpretation: On a temperature-time graph, the flat sections represent the latent heat being absorbed or released. The longer the flat section, the more energy is required for that specific state change.

• Multi-step Problems: Some problems require calculating energy for a temperature rise AND a state change. In these cases, calculate each energy component separately and sum them ($E_{total} = mc\Delta\theta + mL$).

• The 'Constant Temperature' Trap: A common mistake is assuming that if you are heating something, the temperature must be rising. During a phase change, the temperature remains perfectly constant until the entire mass has changed state.

• Confusing Stores: Students often think potential energy is only for gravity. In thermodynamics, potential energy refers to the 'hidden' energy in the bonds/forces between particles.

• Formula Misuse: Do not use the temperature change ($\Delta\theta$) in the latent heat formula. $E = mL$ does not involve temperature because the temperature does not change during the process.