THERMODYNAMIC VARIABLES: WHAT THEY ARE AND SOLVED EXERCISES - PHYSICAL - 2024

The thermodynamic variables or state variables are those macroscopic quantities characterizing a thermodynamic system, the most familiar pressure, volume, temperature and mass. They are very useful in describing systems with multiple inputs and outputs. There are numerous equally important state variables, apart from those already mentioned. The selection made depends on the system and its complexity.

An airplane full of passengers or a car can be considered as systems and their variables include, in addition to mass and temperature, the amount of fuel, geographical position, speed, acceleration and of course many more.

Figure 1. An airplane can be studied as a thermodynamic system. Source: Pixabay.

If so many variables can be defined, when is a variable considered state? Those in which the process by which the variable acquires its value does not matter are considered as such.

On the other hand, when the nature of the transformation influences the final value of the variable, it is no longer considered as a state variable. Important examples of these are work and heat.

The knowledge of the state variables allows to physically describe the system in a given time t _o. Thanks to experience, mathematical models are created that describe their evolution over time and predict the state at time t> t _o.

Intensive, extensive and specific variables

In the case of a gas, which is a system frequently studied in thermodynamics, mass is one of the main state and fundamental variables of any system. It is related to the amount of matter it contains. In the International System it is measured in kg.

Mass is very important in a system and thermodynamic properties are classified according to whether or not they depend on it:

-Intensive: they are independent of mass and size, for example temperature, pressure, viscosity and in general those that distinguish one system from another.

-Extensive: those that vary with the size of the system and its mass, such as weight, length and volume.

-Specific: those obtained by expressing extensive properties per unit of mass. Among them are specific gravity and specific volume.

To distinguish between the types of variables, imagine dividing the system into two equal parts: if the magnitude remains the same in each, it is an intensive variable. If it is not, its value is cut in half.

-Pressure, volume and temperature

Volume

It is the space occupied by the system. The unit of volume in the International System is the cubic meter: m ³. Other widely used units include cubic inches, cubic feet, and the liter.

Pressure

It is a scalar magnitude given by the quotient between the perpendicular component of the force applied to a body and its area. The unit of pressure in the International System is the newton / m ² or Pascal (Pa).

In addition to the Pascal, the pressure has numerous units that are used according to the area. These include psi, atmosphere (atm), bars, and millimeters of mercury (mmHg).

Temperature

In its interpretation at the microscopic level, temperature is the measure of the kinetic energy of the molecules that make up the gas under study. And at the macroscopic level it indicates the direction of the heat flow when putting two systems in contact.

The temperature unit in the International System is the Kelvin (K) and there are also the Celsius (ºC) and Fahrenheit (ºF) scales.

Solved exercises

In this section, equations will be used to obtain the values ​​of the variables when the system is in a particular situation. It's about the equations of state.

An equation of state is a mathematical model that makes use of the state variables and models the behavior of the system. An ideal gas is proposed as an object of study, which consists of a set of molecules capable of moving freely but without interacting with each other.

The proposed equation of state for ideal gases is:

Where P is the pressure, V is the volume, N is the number of molecules, and k is the Boltzmann constant.

-Exercise 1

You inflated your car's tires to the manufacturer's recommended pressure of 3.21 × 10 ⁵ Pa, in a place where the temperature was –5.00 ° C, but now you want to go to the beach, where it is 28 ° C. With the increase in temperature, the volume of a tire has increased by 3%.

Figure 2. When the temperature increases from -5ºC to 28ºC, the air in the tires expands and if there are no losses. the pressure increases. Source: Pixabay.

Find the final pressure in the tire and indicate if it has exceeded the tolerance given by the manufacturer, which is not to exceed 10% of the recommended pressure.

Solution

The ideal gas model is available, therefore the air in the tires will be assumed to follow the given equation. It will also assume that there are no air leaks in the tires, so the number of moles is constant:

The condition that the final volume has increased by 3% is included:

Known data is substituted and final pressure cleared. Important: the temperature must be expressed in Kelvin: T (K) = T (° C) + 273.15

The manufacturer has indicated that the tolerance is 10%, therefore the maximum value of the pressure is:

You can safely travel to the beach, at least as far as the tires are concerned, since you have not exceeded the established pressure limit.

Exercise 2

An ideal gas has a volume of 30 liters at a temperature of 27 ° C and its pressure of 2 atm. Holding the pressure constant, find its volume when the temperature passes -13 ºC.

Solution

It is a constant pressure process (isobaric process). In such a case the ideal gas equation of state simplifies to:

This result is known as Charles's law. The data available are:

Solving for and substituting:

References

1. Borgnakke. 2009. Fundamentals of Thermodynamics. 7 ^th Edition. Wiley and Sons. 13-47.
2. Cengel, Y. 2012. Thermodynamics. 7 ^ma Edition. McGraw Hill. 2-6.
3. Fundamental concepts of thermodynamic systems. Recovered from: textscientificos.com.
4. Engel, T. 2007. Introduction to Physicochemistry: Thermodynamics. Pearson. 1-9.
5. Nag, PK 2002. Basic and Applied Thermodynamics. Tata McGraw Hill. 1-4.
6. Navojoa University. Basic Physicochemistry. Recovered from: fqb-unav.forosactivos.net