TRABALHO NAS TRANSFORMAÇÕES GASOSAS - TERMOLOGIA - Aula 14 - Prof. Boaro

Introduction to Thermodynamics

Overview of the Course

• Professor Marcelo Boaro introduces himself and the topic of thermodynamics, marking this as lesson 14 in the series.

• He reviews previous lessons covering definitions of heat, temperature scales (Celsius, Fahrenheit, Kelvin), thermal expansion in solids and liquids, and modes of heat transfer: conduction, radiation, and convection.

Work Done by Gases

• The focus shifts to work done by gases; he references earlier discussions on gas equations (PVT relationships).

• The professor explains that energy is supplied to a gas in a container causing it to expand and perform work. This concept is crucial for understanding thermal machines.

Understanding Gas Expansion

Mechanics of Gas Expansion

• A visual representation is introduced with a piston in a horizontal cylinder where gas receives heat from a Bunsen burner.

• As the gas expands due to heating, it moves the piston from an initial position to a final position, increasing its volume while maintaining the same amount of gas.

Constant Pressure Scenario

• The discussion emphasizes analyzing work done at constant pressure during gas expansion despite changes in volume.

• The professor clarifies how energy input leads to displacement without altering pressure through careful management of volume changes.

Work Calculation

Force and Displacement Relationship

• He connects concepts from mechanics regarding work: defined as force multiplied by displacement.

• The formula for work includes cosine of the angle between force and displacement vectors; initially assuming they are aligned (angle = 0).

Deriving Mathematical Expressions

• Simplification occurs when considering force acting along displacement direction; thus cosine equals one.

• To derive further expressions for work done by gases under constant pressure conditions, he discusses multiplying terms related to area.

Pressure Conceptualization

Relating Force Over Area

• The relationship between force and area is established as pressure (P = F/A), linking back to prior studies on hydrostatics.

Understanding Gas Transformations and Work

Volume Variation in Gas Transformations

• The volume variation ( Delta V ) of a gas is defined as the area of the base multiplied by height, indicating changes from an initial to a final volume.

Work in Isobaric Processes

• In gas transformations at constant pressure (isobaric), work done is calculated as W = P Delta V .

• During gas expansion, both force and displacement are in the same direction, resulting in positive work since cos(0°) = 1 .

Compression vs. Expansion

• In gas compression, the displacement occurs against the force exerted by the gas, leading to negative work because cos(180°) = -1 .

• The sign of work varies: positive for expansion (work motor) and negative for compression (work resistant).

Importance of Graphical Analysis

• Understanding graphs relating pressure and volume is crucial; areas under these curves represent work done during transformations.

Isothermal vs. Isovolumetric Processes

• For isothermal processes where pressure remains constant, P Delta V = nRDelta T , linking temperature change directly to work done.

• No work occurs during isovolumetric processes since there’s no change in volume.

Calculating Work from Graph Areas

• The area under a pressure-volume graph represents the work done; it can be calculated as base times height when dealing with rectangular shapes.

• This area calculation applies universally across transformations, providing a numerical value for work performed.

Units of Measurement

Understanding Work in Thermodynamics

The Unit of Work in the International System

• The unit of work in the International System is the Joule, although calories are also commonly encountered due to their relation to energy exchanged by gases.

Positive and Negative Work

• When a gas expands from state A to B, the work done is positive; conversely, if it compresses from B back to A, the work is negative.

Calculating Work from Graphical Representations

• The work can be calculated as the area under a pressure-volume graph. This requires understanding how to compute areas for various shapes (rectangles, triangles, trapezoids).

• For curves or complex shapes, integral calculus may be necessary to determine the area accurately.

Understanding Cyclic Transformations

• A cyclic transformation involves a gas returning to its original state after passing through different states of pressure, volume, and temperature.

• To calculate work during a cyclic process, one must find the area enclosed within the cycle on a P-V diagram.

Area Under Curves and Work Calculation

• The area inside any closed figure on a P-V diagram represents the net work done during that cycle.

• If transformations occur in different sequences (e.g., A-B-C-A vs. A-C-B-A), they yield equal magnitudes of work but opposite signs due to expansion and compression dynamics.

Detailed Example of Work Calculation

• In calculating work from point A to B (expansion), one finds positive work represented by an area above the axis; while moving from C back to A results in negative work due to volume decrease.

• The total work for a complete cycle can be expressed as A1 + A2 - A3, where each term corresponds to specific areas representing expansions or compressions.

Directionality of Cycles and Their Impact on Work

Understanding Work in Thermodynamics

Positive and Negative Work

• The concept of work is introduced, explaining that work is positive when done in a counterclockwise direction and negative when done clockwise.

• Emphasis on understanding the material step by step through exercises, with a reference to an upcoming application exercise.

Application Exercise Overview

• An application exercise involving the transformation of a gas behaving as an ideal gas is presented, focusing on a pressure versus volume graph.

• The transformation from state A to B is identified as isotermic, with specific values for pressure (Pa) and volume (Va), noting that volume at state B (VB) equals 3Va.

Calculating Pressure and Work

• To find the pressure PB at state B, the relationship between pressures and volumes during isotermic transformations is utilized: Pa * Va / Ta = PB * VB / Tb.

• It’s noted that since the volume decreases from B to C, this results in negative work. The formula simplifies due to equal temperatures.

Detailed Calculation Steps

• The calculation for PB leads to PB = Pa/3. This value will be used for further calculations regarding work.

• For calculating work done during transformation BC, two methods are suggested: using area under the graph or applying the formula involving pressure and change in volume.

Final Insights on Problem-Solving

• Importance of expressing answers based on given data is highlighted; even if not explicitly stated, responses should reflect provided information.

• The final expression for work calculated as -2/3 * Pa * Va emphasizes clarity in problem-solving methodology.

Additional Resources