PAG: Investigating Specific Heat Capacity

Specific Heat Capacity ($c$): Defined as the amount of thermal energy required to raise the temperature of $1$ kg of a substance by $1$ K (or $1$ °C) without a change in state. It is measured in units of $J \, kg^{-1} \, K^{-1}$.

Thermal Energy Transfer: The relationship between energy change ($\Delta E$), mass ($m$), and temperature change ($\Delta \theta$) is governed by the equation $\Delta E = m c \Delta \theta$.

Electrical Power Input: In a laboratory setting, energy is typically supplied by an immersion heater where the energy $E$ is calculated from the potential difference ($V$), current ($I$), and time ($t$) using $E = IVt$.

Setup: Place the substance (solid block or liquid in a beaker) on a digital balance to record its mass ($m$). Insulate the container with a low-conductivity material like cotton wool or polystyrene to minimize heat loss.

Instrumentation: Connect an immersion heater to a power supply in series with an ammeter and in parallel with a voltmeter. Insert a thermometer into the substance.

Procedure: Record the initial temperature. Turn on the power and start a stopwatch simultaneously. Record the voltage ($V$) and current ($I$) at regular intervals, ensuring they remain constant.

Data Collection: Heat the substance for a fixed duration (e.g., 10 minutes). Turn off the heater but continue monitoring the thermometer until the temperature stops rising to capture the true maximum value.

Graphical Approach: Plot a graph of Temperature ($\theta$) on the y-axis against Time ($t$) on the x-axis. The gradient of the linear portion represents the rate of temperature increase ($\frac{\Delta \theta}{\Delta t}$).

Calculation: Using the power $P = IV$, the specific heat capacity is calculated as $c = \frac{P}{m \times \text{gradient}}$.

Alternative Method: Plot Energy Supplied ($E = IVt$) on the y-axis against the product of mass and temperature change ($m\Delta\theta$) on the x-axis. In this case, the gradient of the resulting straight line is directly equal to the specific heat capacity ($c$).

Identify the Gradient: When using a graph, always use the linear section. The initial curve is due to the heater warming up, and the later curve is due to increased heat loss as the substance gets hotter.

Heat Loss Impact: If heat is lost to the surroundings, the measured temperature change ($\Delta \theta$) will be lower than expected for a given energy input. This results in an overestimation of the specific heat capacity.

Sanity Check: Water has a very high $c$ (approx. $4200 \, J \, kg^{-1} \, K^{-1}$), while metals are much lower (e.g., Aluminum $\approx 900$, Copper $\approx 390$). If your calculated value for a metal is in the thousands, check for missing insulation or calculation errors.

Uncertainty: Always check the resolution of your instruments. A thermometer with $0.1$ °C resolution is preferred over $1$ °C to reduce percentage uncertainty in $\Delta \theta$.