How is Specific Heat Capacity Measured?

Specific heat capacity is typically measured by determining the heat capacity of a sample of the substance, usually with a calorimeter, and then dividing that value by the sample's mass.

Measuring specific heat capacity is a fundamental process in thermodynamics, allowing scientists and engineers to understand how different materials absorb or release heat. The core principle, as described in the reference, involves relating the heat absorbed or released by a substance to its resulting temperature change.

The Measurement Process

The standard method relies on the definition of specific heat capacity ($c$), which is the heat capacity ($C$) of a sample divided by its mass ($m$):

$c = \frac{C}{m}$

The heat capacity ($C$) of a sample is the amount of heat energy ($\Delta Q$) required to raise its temperature by one degree Celsius (or Kelvin, as the change is the same). It can be expressed as:

$C = \frac{\Delta Q}{\Delta T}$

where $\Delta T$ is the change in temperature.

Combining these definitions, the specific heat capacity can be found using the formula:

$c = \frac{\Delta Q}{m \Delta T}$

This means that to measure specific heat capacity, one needs to measure:

• The amount of heat energy ($\Delta Q$) added to or removed from the sample.
• The mass ($m$) of the sample.
• The resulting change in temperature ($\Delta T$) of the sample.

Using a Calorimeter

A crucial tool for measuring specific heat capacity is the calorimeter.

• What is a Calorimeter? A calorimeter is a device designed to measure the heat transferred during a process. It typically consists of an insulated container to minimize heat exchange with the surroundings, a thermometer to measure temperature changes, and often a stirrer to ensure uniform temperature distribution.
• How it's Used:
  1. A known mass ($m$) of the substance is placed inside the calorimeter.
  2. A measured amount of heat ($\Delta Q$) is added to (or removed from) the substance. This can be done electrically (by a heating element) or by mixing with another substance of known temperature and specific heat (like water, using the principle of conservation of energy where heat lost by one substance equals heat gained by the other).
  3. The initial and final temperatures are recorded to find the temperature change ($\Delta T$).
  4. Using the measured $\Delta Q$, $m$, and $\Delta T$, the specific heat capacity $c$ is calculated using the formula $c = \frac{\Delta Q}{m \Delta T}$.

Example Measurement Steps

Here's a simplified look at a common method using water and a calorimeter (known as calorimetry by mixing):

1. Measure the mass ($m_{sample}$) of the substance whose specific heat is to be determined.
2. Heat the sample to a known initial temperature ($T_{sample, initial}$).
3. Place a known mass ($m{water}$) of water at a known initial temperature ($T{water, initial}$) into the calorimeter.
4. Carefully transfer the hot sample into the water inside the calorimeter.
5. Stir the mixture and record the final equilibrium temperature ($T_{final}$) once it stabilizes.
6. Calculate the temperature changes:
   • $\Delta T{sample} = T{final} - T_{sample, initial}$
   • $\Delta T{water} = T{final} - T_{water, initial}$
7. Assume that the heat lost by the sample equals the heat gained by the water (and the calorimeter, if its heat capacity is known and significant).
   • Heat lost by sample ($\Delta Q{sample}$) = $m{sample} \times c{sample} \times \Delta T{sample}$
   • Heat gained by water ($\Delta Q{water}$) = $m{water} \times c{water} \times \Delta T{water}$ (where $c_{water}$ is the known specific heat of water, approx. 4186 J/kg°C)
8. Set the heat lost equal to the heat gained (ignoring calorimeter for simplicity): $|\Delta Q{sample}| = \Delta Q{water}$.
9. Solve for the specific heat capacity of the sample ($c_{sample}$).

This method directly applies the principle described in the reference, measuring heat transfer and temperature change within a controlled environment to determine heat capacity per unit mass.