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# Heat Capacity and Internal Energy in Thermodynamics

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Last updated date: 12th Jul 2024
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## Thermodynamics

Thermodynamics is a branch of physics that studies  function, heat, and temperature, as well as their relationships with radiation, electricity, and matter's physical properties.

Thermodynamics is used in a broad range of scientific and engineering disciplines, including physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as more complex areas including meteorology.

The theory of the relationship between heat, work, temperature, and energy is known as thermodynamics. Thermodynamics, in its broadest sense, is concerned with the transition of energy from one location to another and from one type to another. The three laws of thermodynamics govern the behaviour of these quantities, and provide a quantitative definition using observable macroscopic physical quantities but can be described by statistical mechanics in terms of microscopic constituents.

The first theorem of thermodynamics, also known as the law of energy conservation. The difference in a system’s internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings.

The second law of thermodynamics describes how heat is transferred from one place to another. Heat does not naturally flow from a cooler to a hotter area, or, to put it another way, heat at a given temperature cannot be turned entirely into function.

The Third Law of Thermodynamics is one of the most important laws of thermodynamics.

If the temperature reaches absolute zero, the entropy of a perfect crystal of an atom in its most stable state tends to zero.

In this article, we will discuss the sub-topic of thermodynamic, heat capacity and internal energy.

### Internal Energy of Thermodynamics

The energy found within a thermodynamic device is known as its internal energy.

It's the amount of energy used to construct or plan a structure in any given internal state. It excludes the kinetic energy of the system's motion as a whole, as well as the potential energy of the system as a whole due to external force fields, which includes the energy of movement of the system's surroundings. It maintains track of the system's energy benefits and losses as a result of changes in its internal environment. The difference between a reference zero specified by a normal state and the internal energy is determined.

Internal energy is a broad property that cannot be directly determined.

Transfers of matter or energy as heat, as well as thermodynamic function, are the thermodynamic processes that characterise internal energy. Changes in the system's several factors, such as entropy, volume, and chemical composition, are used to calculate these processes.

The internal energy formula is written as U = Q W in equation form.

The change in the internal energy formula U of the device is represented by ΔU. The number of all heat flow into and out of the system is Q, which is the net heat transmitted into the system. W denotes the system's network or the amount of all work performed on or by the system. The internal energy equation is used to calculate the change in the internal energy of a gas.

The internal energy equation in thermodynamics is also called the first law of thermodynamics equation is ΔU = Q − W.

The internal energy of a closed thermodynamic system.

The differentials of each expression can be used to express this relationship in infinitesimal terms, but only the internal energy is an exact differential.

The change in internal energy for a closed system with only heat and work transfers is

δU = δQ - δW

The first law of thermodynamics is expressed in this way.

Other thermodynamic parameters should be used to express it. Each word is made up of an intensive variable (a generalised force) and an infinitesimal extensive variable that is conjugate to it (a generalised displacement).

The mechanical work performed by the machine, for example, can be connected to the pressure P and volume shift δV. The volume shift is the substantial generalised displacement, while the pressure is the intensive generalised force:

δW = PδV

This defines the direction of work W, to be energy transfer from the working device to the surroundings, indicated by a positive term.

Taking the direction of heat transfer Q to be into the working fluid and assuming a reversible mechanism, the heat is,

δQ = TδS

Where T denotes the temperature

S denotes the entropy.

Hence the change in internal energy formula thermodynamics is,

δU = TδS - PδV

### Heat Capacity in Thermodynamics

Heat capacity, also known as thermal capacity, is a physical property of matter defined as the amount of heat required to cause a unit change in temperature in a given mass of a substance.

The joule per kelvin (J/K) is the SI unit of heat capacity.

The term "heat capacity" refers to a wide range of characteristics. The basic heat potential is the intense property that corresponds. The molar heat capacity is calculated by dividing the heat capacity by the volume of a substance in moles. The heat capacity per volume is measured by the volumetric heat capacity. Thermal mass is a term used in architecture and structural engineering to describe a building's heat capacity in thermodynamics.

According to the first law of thermodynamics, heat supplied to the device contributes to both the work done and the change of internal energy at constant pressure.

The heat capacity is denoted by the letter C$_{p}$.

Heat capacity at constant volume, dV = 0, dQ = dU (isochoric process)

The heat supplied The heat capacity in thermodynamic is an object, denoted by Q, hence the heat capacity equation is followed as,

C = $\frac{\Delta Q}{\Delta T}$

Where,

C: Heat capacity

$\Delta$Q: Total energy

$\Delta$T: Change in temperature

Heat capacities for a homogeneous system that is subjected to various thermodynamic processes.

Heat capacity at constant pressure, dQ = dU + PdV (Isobaric process)

would only add to the change in internal energy in a device performing a phase at constant volume and no work would be completed.

C$_{v}$ is the heat capacity obtained in this manner. The value of Cv  is never greater than the value of C$_{p}$.

## FAQs on Heat Capacity and Internal Energy in Thermodynamics

Q.1. Are Internal Energy and Heat Energy the Same?

Answer: The terms 'thermal' and 'heat' refer to the same thing.

The terms 'internal' and 'thermal' energy are not synonymous, but they are linked. The sum of the spontaneous distribution of the kinetic and potential energies of the molecules/atoms in a substance is known as internal energy.

Q.2. What Is the Relationship Between Heat Capacity and Specific Heat Capacity?

Answer: The heat capacity and the specific heat are related by C = cm or c = C/m. The mass m, specific heat c, change in temperature ΔT, and heat added (or subtracted) Q are related by the equation: Q=mcΔT. Values of specific heat are dependent on the properties and phase of a given substance.