when to use q=mc ΔT and when to use q=CΔT

The equation q=mcΔT is used to calculate the heat energy (q) transferred during a process where the temperature change (ΔT) occurs in a system with a constant mass (m) and specific heat capacity (c).

This equation is applicable when we have a system with a known mass and want to determine the amount of heat energy gained or lost due to a temperature change. The specific heat capacity (c) represents the amount of heat energy required to raise the temperature of one unit mass of a substance by one degree Celsius (or Kelvin).

For example, let's consider heating a sample of water. The equation q=mcΔT can be used to calculate the amount of heat energy required to raise the temperature of the water by a certain amount. Here, m represents the mass of the water, c represents the specific heat capacity of water (4.18 J/g·°C), and ΔT represents the change in temperature.

On the other hand, the equation q=CΔT is used to calculate the heat energy (q) transferred during a process where the temperature change (ΔT) occurs in a system with a constant heat capacity (C).

Heat capacity (C) is an extensive property that represents the amount of heat energy required to raise the temperature of an entire system by one degree Celsius (or Kelvin). It depends on the mass and specific heat capacity of the substance or substances in the system.

When we want to calculate the amount of heat energy gained or lost by a system as a whole, regardless of the individual masses or specific heat capacities of the components, we can use the equation q=CΔT. This equation considers the total heat capacity of the system.

For instance, in a calorimetry experiment, where the heat exchange occurs between two substances in a calorimeter, we use the equation q=CΔT to determine the amount of heat gained or lost by the combined system. The heat capacity (C) in this case represents the sum of the individual heat capacities of the substances involved.

It's important to note that the specific heat capacity (c) is a property specific to a substance, while the heat capacity (C) is a property of a system. The specific heat capacity is typically used when dealing with individual components, while the heat capacity is used when considering the entire system.

In summary, we use the equation q=mcΔT when calculating the heat energy transferred in a process with a constant mass and specific heat capacity. On the other hand, we use the equation q=CΔT when calculating the heat energy transferred in a process with a constant heat capacity, considering the entire system. The choice between the two equations depends on whether we are focusing on individual components with known masses and specific heat capacities or the system as a whole.