The heat produced over a specific time period can be determined using the formula:

$Q = mc\Delta T$

In this equation, $Q$ represents the heat energy, $m$ denotes the mass of the substance, $c$ indicates the specific heat capacity, and $\Delta T$ signifies the change in temperature.

This formula is grounded in the principle of conservation of energy, which asserts that energy cannot be created or destroyed; it can only be transferred or transformed. In the realm of heat energy, this principle implies that the heat energy generated by a system is equivalent to the heat energy absorbed by that system.

The variables in the formula are defined as follows:

• $Q$: the heat energy produced or absorbed, measured in joules ($J$);
• $m$: the mass of the substance being heated or cooled, measured in kilograms ($kg$);
• $c$: the specific heat capacity of the substance, which quantifies the amount of heat energy needed to raise the temperature of $1 kg$ of the substance by $1 \degree C$, measured in joules per kilogram per degree Celsius ($J/(kg \cdot \degree C)$);
• $\Delta T$: the change in temperature, measured in degrees Celsius ($\degree C$).

To calculate the heat produced over a specified time period, you must first measure or know the mass of the substance, its specific heat capacity, and the temperature change during that time. You can then substitute these values into the formula to compute the heat energy.

For instance, if you were heating $2 kg$ of water (which has a specific heat capacity of $4200 J/(kg \cdot \degree C)$) from $20 \degree C$ to $100 \degree C$, the heat energy produced would be calculated as follows:

$Q = 2 \, kg \times 4200 \, \frac{J}{kg \cdot \degree C} \times (100 \degree C - 20 \degree C) = 672,000 \, J$

It is important to note that this formula assumes no heat energy is lost to the surrounding environment. In practical situations, some heat energy will invariably be lost, meaning that the actual heat energy produced may be less than the calculated value.