Heat Capacity

It has been detected experimentally that within a certain state of matter, the change in temperature of a substance increases proportional to the supplied energy, i.e. the following law can be applied: $$\boxed{\Delta Q = C \Delta T}$$ The proportional constant $C$ is called heat capacity. This law already indicates that there is a direct relationship between temperature and the inner energy of gases for instance. The heat capacity of a body depends in particular on the composition of the substance. If it consists of a homogeneous material, a so-called specific heat capacity $c$ can be defined, which can be interpreted as heat capacity per mass. This means that the relationship between $\Delta Q$ and $\Delta T$ can be written as: $$\boxed{\Delta Q = cm\Delta T}$$ In the literature, the unit of $c$ is usually given as $\mathrm{kJ}/(\mathrm{kg}\cdot K)$. If you multiply the specific heat capacity of a body with its mass, you get the heat capacity $C$ with the unit kJ/K. The energy can be supplied to the system in different ways. For example, friction losses or electrical currents can be used to heat up a body, a liquid, or a gas. If an object for instance falls from a certain height into a pool of water, all of the potential energy is converted into thermal energy, so that the water experiences a small, barely measurable, increase in temperature. In the case of electrical heating, the power output must be multiplied by the time $\Delta t$ to get $\Delta Q$. From this one can compute the required time for heating up a system with the mass $m$ with the power $P$: $$\boxed{\Delta t = \frac{cm\Delta T}{P}}$$ When using this formula, it is important that the power output is constant over time, which is always approximately the case with electrical consumers such as water boilers.

• Heat Capacity of Water (+)