Dimensionless Heat Capacity

Heat was once assumed to be fluid before the advent of current thermodynamics. Joseph Black, around the 1750s, coined the word heat capacity to describe the ability of bodies to hold a specific amount of this fluid. Instead, today’s focus is on a system’s inherent energy. This consists of potential energy and kinetic energy at the microscopic level. Heat, however, is no longer regarded as a liquid. Rather, it is a tiny transmission of disordered energy. Nonetheless, the word “heat capacity” endures, at least in English. The article below will briefly discuss heat capacity, specific heat, and dimensionless heat capacity. 

Heat Capacity: What is it?

If you keep a metal chair outside in the direct sun on a hot summer day, it gets pretty heated up. On the contrary, a similar mass of water exposed to the same amount of sunlight will not get nearly as heated. This means water has a high heat capacity, which means it can hold a lot of heat. It brings us to one of the essential physical properties of substances, referred to as heat capacity.

The measurable physical property that characterises the amount of heat necessary to change a system’s temperature by a particular amount is heat capacity (typically indicated by a capital C). It is also referred to as thermal capacity. 

By definition, the ratio of the quantity of heat supplied to the object (Q) to the subsequent temperature increase of the object (△T) is the heat capacity (C) of that particular object. It is given by the formula: C= Q/ △T

A system’s heat capacity is determined by the kind of material it is made of as well as its mass. An object having a greater mass has a higher heat capacity. So, to change one unit of temperature, an object with a larger heat capacity requires more heat.

Unit of Heat Capacity

The heat capacity unit of an object in the SI system is Joules per Kelvin (J/K). An increase of one degree Celsius is equivalent to a temperature increase of one Kelvin, so the value of J/°C remains the same.

Specific Heat Capacity

The specific heat capacity of a sample is given by its heat capacity, divided by its mass in thermodynamics. The other term used for specific heat capacity is massic heat capacity.

Precisely, it is the quantity of heat that must be supplied to a unit of mass of a substance to achieve a one-unit temperature increase. You can measure the specific heat capacity of a substance using the formula given below:

Q= mc△T, 

where m = substance’s mass in kg,

C = specific heat capacity of the substance given by J/(kg°C) or J/(kg K),

△T = change in temperature in °C  or K,

And Q = thermal energy required to change the temperature of the substance, given in Joules (J). 

Unit of Specific Heat Capacity

The specific heat capacity unit in the SI system is J/(kg°C) or J/(kg K).

Water, for example, has a specific heat capacity of 4200 J/kg/°C, which means it takes 4200J of heat energy to raise the temperature of 1kg of water by 1°C.

Dimensionless Heat Capacity

The dimensionless heat capacity of an ideal gas is directly proportional to half the number of degrees of freedom for each particle. As a result of the equipartition theorem, this applies to quadratic degrees of freedom. In general, it associates the logarithmic rise in temperature with the rise in dimensionless entropy per particle. 

An object’s dimensionless heat capacity is given by C* = C/NkB

Or, C* = C/nR.

Where

C = the heat capacity of a system composed of a particular material (J/K),

N = number of molecules in the system (dimensionless),

kB = Boltzmann constant (J/K),

n = the amount of material in the system (mol),

R = gas constant (J/K/mol).

Heat capacity and specific heat capacity: Know the difference

The quantity of heat needed to increase the temperature of a substance by one degree Celsius is known as heat capacity. On the other hand, the quantity of heat required to increase the temperature of 1 gramme of a substance by 1 degree Celsius is known as its specific heat. So, the heat capacity of a substance is not dependent on its mass. But the specific heat capacity directly depends on the mass of the substance. 

Moreover, the heat capacity unit and specific heat capacity units are different. The SI unit of heat capacity is Joules/ Kelvin (J/K). In contrast, the specific heat capacity unit in the SI system is J/ (kg K). Since a temperature increase of one degree Celsius is equivalent to a temperature increase of one Kelvin, J/°C and J/K are the same.

Conclusion

Heat capacity, in Physics, is the quantity of heat required for the rise in temperature of a system by 1°C. It is among the most vital thermodynamic properties of metals, as it aids in the prediction of entropy and enthalpy of material. The difference between heat capacity and specific heat is that the former is an extensive property that depends on the size of the system. The latter is an intensive property. The non-dimensional heat capacity associates the logarithmic rise in temperature with the rise in dimensionless entropy per particle.