SPECIFIC HEAT CAPACITY BY MR. WONG

1. The Specific Heat Capacity Equation

The standard formula used to calculate heat energy transfer in a system is:
$Q = m C \Delta T$

• Variable Definitions and Units:

  • $Q$: Heat energy, measured in Joules ($\text{J}$).

  • $m$: Mass of the substance, measured in grams ($\text{g}$) or kilograms ($\text{kg}$).

  • $C$: Specific heat capacity, which is the energy required to raise the temperature of 1 unit of mass by 1 degree.

  • $\Delta T$: Change in temperature, defined as:
    $\Delta T = T<em>F - T</em>I$

  • $T_F$: Final temperature

  • $T_I$: Initial temperature

2. Using the Formula Triangle Method

When solving for different unknown variables without performing full algebraic rearrangement every time, you can use the formula triangle (with $Q$ at the top, and $m$, $C$, and $\Delta T$ along the bottom):

1. Solving for Mass ($m$):

   • Cover $m$ in the triangle.

   • Rearranged equation:
     $m = \frac{Q}{C \Delta T}$

2. Solving for Specific Heat Capacity ($C$):

   • Cover $C$ in the triangle.

   • Rearranged equation:
     $C = \frac{Q}{m \Delta T}$

3. Solving for Change in Temperature ($\Delta T$):

   • Cover $\Delta T$ in the triangle.

   • Rearranged equation:
     $\Delta T = \frac{Q}{m C}$

4. Solving for Final Temperature ($T_F$):

   • First find $\Delta T$ using $\Delta T = \frac{Q}{m C}$.

   • Substitute $\Delta T = T<em>F - T</em>I$ and solve for $T<em>F$: $T</em>F = \frac{Q}{m C} + T_I$

3. Sign Conventions for Heat ($Q$)

The sign of $Q$ indicates whether energy is entering or leaving the system:

• Positive Heat ($+Q$): Endothermic process. Heat is absorbed by the system, increasing its temperature.

• Negative Heat ($-Q$): Exothermic process. Heat is given off or released by the system, decreasing its temperature.

4. Application to Calorimetry Labs

In lab experiments involving heat exchange between two substances (such as a warm metal placed into water):

• Law of Conservation of Energy: Thermal energy lost by one substance is gained by the other.

• Heat Relationship:

  • If water absorbs heat, its heat value is positive ($+Q_{\text{water}}$).

  • The metal releases an equal amount of heat, making its heat value negative ($-Q_{\text{metal}}$).

  • Equation representation:
    $Q<em>{\text{water}} = -Q</em>{\text{metal}}$