Relationship between Cp and Cv

Introduction

Whenever heat is absorbed by a body, this results in an increase in the body’s temperature. And when heat is removed, the temperature decreases. It is possible to quantify the total kinetic energy of the particles that make up an object by measuring the temperature of that entity. Consequently, when heat is absorbed by an item, this heat is converted into the kinetic energy of the particles, causing the temperature to rise. Thus, the change in temperature is proportional to the heat transfer.

It is represented by the formula Q = n C T. The heat Q necessary to produce a T variation in temperature of one mole of any substance is represented by the formula Q = n C T. The constant C in this equation is referred to as the molar heat capacity of the body. As a result, the molar heat capacity of a substance is defined as the amount of heat energy required to change the temperature of one mole of that substance by one unit of temperature. The nature, scale, and makeup of the system all play a role in this.

CP and CV are two different types of molar heat capacities that will be discussed in this article, as well as the link between Cp and Cv.

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IDEAL GAS THEORY

The ideal gas theory is extremely significant for the understanding of processes because in the majority of cases, moisture content is extracted in the form of water vapours, which act in the same way as an ideal gas in most scenarios. There are three factors that can be used to characterise an ideal gas: the volume that it occupies, the pressure that it exerts, and the temperature that it reaches. According to the definition, ideal gas is a special state of matter that can be bounded by a system boundary and is a special state of matter. It is presumptively true that:

• All particles have rest mass (m>0; the particles are not photons; all particles have rest mass).
• The number of particles in relation to the total volume of the system is modest.
• When compared to the whole volume of the system, the total volume of particles is small.

Accidental collisions of particles with one another are far less likely than collisions with the system’s boundary.

When real gases are treated as ideal (under particular conditions), the practical advantage is a straightforward equation of state containing only one constant. A simplified version of the ideal gas equation of state is given below.

PV= mRT

where P denotes atmospheric pressure in Pa, V denotes gas volume in cubic metres, m denotes gas mass in kilogrammes, T denotes gas temperature in degrees Celsius, and R is the gas constant, which is expressed in joules per kilogram of gas per kilogramme of temperature (J/kgK).

What is Cv?

Cv is defined as the quantity of heat energy that a substance absorbs or releases (per unit mass) as a result of a change in temperature when no change in volume takes place. In other words, it is the amount of thermal energy that is exchanged between a system and its surroundings without any change in the volume of the system being transferred.

This word refers to the amount of internal energy that a system has. The internal energy of a system is equal to the total of its potential and kinetic energy. Changes in the temperature of a system can cause the system to either absorb or release energy into the surrounding environment. Specifically, if this change in internal energy occurs while the volume remains constant, then it is known as the specific heat at constant volume (Cv).

Cv=dU/dt

where Cv is the specific heat at a constant volume (or a constant temperature), dU is the change in internal energy.

The temperature change is represented by the symbol dt.

What is Cp?

The specific heat at constant pressure is denoted by the symbol Cp. It is the amount of energy produced or absorbed by a unit mass of a substance when the temperature of the substance changes while the pressure remains constant. In other words, it is the energy transmitted between a system and its environment when the system is subjected to continuous pressure.

This phrase has something to do with the enthalpy of a given system. The amount of energy received or emitted is measured as enthalpy. It is defined as the sum of the internal energy and the product of pressure and volume, plus a small amount of additional energy. This is due to the fact that the total quantity of energy that a system absorbs or releases is equal to the amount of energy that the system already has (internal energy) plus the amount of changes that occur in the system (PV). As the temperature of the system changes, the enthalpy of the system will change as well. As a result, the following can be presented.

Cp=dH/dt

where, the specific heat at constant pressure is denoted by the symbol Cp, the enthalpy change is represented by the symbol dH, the temperature change is represented by the symbol dt.

Relationship Between CV and CP

Taking into consideration a substance’s ideal gas behaviour, the following link can be established:

R is equal to CP – CV.

In this equation, r denotes the universal gas constant.

The ratio between CP and CV is the specific heat ratio, γ.

R= CP /CV

Conclusion

Specific heats are thermodynamic properties of substances that are measured in degrees Celsius. These characteristics explain the behaviour of a substance or a system in response to changes in the temperature of that substance or system When applied to ideal gases, the concept of specific heat is correct; however, when applied to actual gases, it must frequently be adjusted. This is due to the fact that the behaviour of gases is often determined by both temperature and pressure.

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