Specific heat capacity Knowledge-Based Study

Study notes

1. To understand specific heat capacity, it is essential to distinguish between temperature and heat.

   • Temperature is an intensive property that reflects the average kinetic energy of the particles within a substance.
   • Thermal energy is an extensive property representing the total kinetic and potential energy of all particles in a sample.
   • Heat ($q$) is the transfer of thermal energy between systems at different temperatures, flowing spontaneously from a warmer region to a cooler region until thermal equilibrium is reached.

   When equal quantities of heat are supplied to equal masses of different materials, their temperatures do not increase at the same rate. This response depends on a characteristic property known as heat capacity.

   Heat capacity ($C$) is the quantity of heat required to raise the temperature of an entire object by $1^\circ\text{C}$ (or $1\text{ K}$). Because heat capacity depends on the mass of the sample, it is an extensive property.

   In contrast, specific heat capacity (commonly designated as $c$) is an intensive property defined as the amount of heat energy required to raise the temperature of exactly one gram of a substance by one degree Celsius (or one Kelvin):

   $$c = \frac{q}{m \cdot \Delta T}$$

   • $q$: Heat absorbed or released ($\text{J}$)
   • $m$: Mass of the sample ($\text{g}$)
   • $c$: Specific heat capacity ($\text{J}\cdot\text{g}^{-1}\cdot^\circ\text{C}^{-1}$)
   • $\Delta T$: Temperature change ($T_{\text{final}} - T_{\text{initial}}$)

   Substances with high specific heat capacities, such as liquid water ($c \approx 4.184\text{ J}\cdot\text{g}^{-1}\cdot^\circ\text{C}^{-1}$), resist temperature changes and store substantial energy. Substances with low specific heat capacities, such as copper ($c \approx 0.385\text{ J}\cdot\text{g}^{-1}\cdot^\circ\text{C}^{-1}$), heat up and cool down much more rapidly.

   Rearranging the definition of specific heat capacity yields the fundamental equation for heat exchange:

   $$q = mc\Delta T$$

   Sign Conventions for Heat Exchange

   • Endothermic process ($q > 0$): Heat enters the system, causing an increase in temperature ($\Delta T > 0$).
   • Exothermic process ($q < 0$): Heat leaves the system, resulting in a decrease in temperature ($\Delta T < 0$).

   Conservation of Energy

   Calorimetry relies on the principle of conservation of energy in an isolated system. In the absence of heat exchange with the surroundings, the net thermal transfer is zero:

   $$q_{\text{system}} + q_{\text{surroundings}} = 0 \implies q_{\text{gained}} = -q_{\text{lost}}$$

   When a heated metal sample is placed into water, thermal energy transfers until both substances reach a common final temperature.