Definition
The heat capacity of an object, denoted by 
, is the limit
where 
is the amount of heat that must be added to the object of mass M in array to raise its temperature by 
.
The proceeds of this parameter usually varies considerably depending on the starting temperature 
of the object as living as the pressure 
applied to it. In particular, it typically varies dramatically with phase transitions such(a) as melting or vaporization see enthalpy of fusion and enthalpy of vaporization. Therefore, it should be considered a function 
of those two variables.
The variation can be ignored in contexts when working with objects in narrow ranges of temperature and pressure. For example, the heat capacity of a block of iron weighing one pound is about 204 J/K when measured from a starting temperature T = 25 °C and P = 1 atm of pressure. That approximate benefit is quite adequate for all temperatures between, say, 15 °C and 35 °C, and surrounding pressures from 0 to 10 atmospheres, because the exact value varies very little in those ranges. One can trust that the same heat input of 204 J will raise the temperature of the block from 15 °C to 16 °C, or from 34 °C to 35 °C, with negligible error.
At constant pressure, heat supplied to the system contributes to both the work done and the modify in internal energy, according to the first law of thermodynamics. The heat capacity is called 
A system undergoing a process at fixed volume implies that no expansion work is done, so the heat supplied contributes only to the change in internal energy. The heat capacity obtained this way is denoted 
The value of 
is always less than the value of
Mayer's relation:
where
Using the above two relations, the particular heats can be deduced as follows:
No change in internal power to direct or instituting to direct or defining as the temperature of the system is constant throughout the process leads to only work done by the a thing that is said supplied heat, and thus an infinite amount of heat is known to add the temperature of the system by a constituent temperature, leading to infinite or undefined heat capacity of the system.
Heat capacity of a system undergoing phase transition is infinite, because the heat is utilized in changing the state of the material rather than raising the overall temperature.
The heat capacity may be well-defined even for heterogeneous objects, with separate parts reported of different materials; such(a) as an electric motor, a crucible with some metal, or a whole building. In numerous cases, the isobaric heat capacity of such objects can be computed by simply adding together the isobaric heat capacities of the individual parts.
However, this computation is valid only when all parts of the object are at the same external pressure previously and after the measurement. That may non be possible in some cases. For example, when heating an amount of gas in an elastic container, its volume and pressure will both increase, even if the atmospheric pressure external the container is kept constant. Therefore, the powerful heat capacity of the gas, in that situation, will have a value intermediate between its isobaric and isochoric capacities 
and 
.
For complex thermodynamic systems with several interacting parts and state variables, or for measurement conditions that are neither constant pressure nor constant volume, or for situations where the temperature is significantly non-uniform, the simple definitions of heat capacity above are not useful or even meaningful. The heat power to direct or determine to direct or instituting that is supplied may end up as kinetic energy energy of motion and potential energy energy stored in force fields, both at macroscopic and atomic scales. Then the change in temperature will depends on the particular path that the system followed through its phase space between the initial andstates. Namely, one must somehow specify how the positions, velocities, pressures, volumes, etc. changed between the initial andstates; and usage the general tools of thermodynamics to predict the system's reaction to a small energy input. The "constant volume" and "constant pressure" heating modes are just two among infinitely numerous paths that a simple homogeneous system can follow.