Thermodynamics ProcessesStuff gets real

Work Correction∆U= Q+W

Variable Sign What it meansQ + Heat has been transferred into the system

- Heat has been removed from the system

W - Work has been done by the system (work has removed energy from the system) System is explanded

+ Work has been done on the system (work has added energy to the system) System is compressed

Due to the shift in sign convention, we also need to say

W=-p∆VPractice Problem

Scenario Q WA system gains heat as work is done on it.A system is compressed while gaining heat from outside the system.A system does not lose any heat while its volume is expanded.A system remains at a constant volume while its temperature increases.

Internal EnergyThis is the kinetic energy of a molecule:

If we want to expand this to know the internal energy of a substance, we use

Story Notes. Completed with material from Knapp Notes and Open Stax Physics Textbook

We can change the internal energy by: Adding (or removing) heat Doing work on the system (or having the system do work) – such as changing the volume of the system.

Practice Problem: Increasing the TemperatureThe temperature of a gas increases from 293° C to 437°C. What is the ratio of the final internal temperature to its initial internal temperature?

Constant Temperature on a PV DiagramPV diagrams are diagrams that plot the pressure of a substance on the y axis and the volume of a gas on the x axis.If a substances is acting like an ideal gas, we can use the ideal gas law to show the relationship between P and V.

P=constant/V

Because P and V are inversely proportional to one another (as one gets larger, the other gets smaller in a closed system).

When you plot inversely proportional variables, you get a hyperbola (see left).

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IsothermsEach hyperbola looks a little different for different temperatures.

This diagram shows the PV diagram for a substances at different temperatures.

Each curve here is called an isotherm- “iso” means “equal” in Latin.

Practice Problem: Isothermal Process An ideal gas is initially in a state that corresponds to point 1 on the graph above, where it has pressure p1, volume V1, and temperature T1. The gas undergoes an isothermal process represented by the curve shown, which takes it to a final state 3 at temperature T3. If T2 and T4 are the temperatures the gas would have at points 2 and 4, respectively, which of the following relationships is true?(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 = T4

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Four Types of ProcessesIsobaric –Constant Pressure Isochoric (isovolumetric)

Volume stays the sameIsothermal-Temperature stays the same

Adiabatic- nothing stays the same

Pressure is constantVolume increases

W=P∆V

What the Graph Looks Like:

Real World Example:

Pressure changesVolume is constant

W= 0J∆U=Q

What the Graph Looks Like:

Real World Example:

Temperature does not changeInternal Energy does not change

∆U=0Q=W

What the Graph Looks Like:

Real World Example:

Happens very fast.No enough time for energy to come in from outside the system. All energy comes from internal energy.

Q=0∆U=-W

What the Graph Looks Like:

Real World Example:

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Work Done On or By a GasMany engines that do work involve pistons and cylinders.Some assumptions about pistons:

The piston can move up and down in the cylinder. Inside the cylinder, under the piston, is a gas. The gas cannot escape around the piston. Push down on the piston and the gas is compressed into a smaller volume. +W Pull up on the piston and the gas expands into a larger volume. -W

Isobaric ProcessHow to identify them: Pressure is constant and the volume is increasing

Keep in mind: Pressure is constantVolume increases

W=-P∆V

Figure 1- Graph of Isobaric Process

Practice Problem: Temperature in Isobaric ProcessesThe volume of a gas is doubled while the pressure remains constant. a) Is the work positive or negative?b) Is the temperature increasing or decreasing?b) Is the internal energy increasing or decreasing?c) Would you expect heat to be added or removed from the system during this process?

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y

G as expands at constant pressurem oving piston a distance o f y

Practice Problem: AP Physics 2007B5

2007B5. The figure above shows a 0.20 m diameter cylinder fitted with a frictionless piston, initially fixed in place. The cylinder contains 2.0 moles of nitrogen gas at an absolute pressure of 4.0 × 105 . Pa. Nitrogen gas has a molar mass of 28 g/mole and it behaves as an ideal gas.a. Calculate the force that the nitrogen gas exerts on the pistonb. Calculate the volume of the gas if the temperature of the gas is 300 K.c. In a certain process, the piston is allowed to move, and the gas expands at constant pressure and pushes the piston out 0.15 m. Calculate how much work is done by the gas.d. Which of the following is true of the heat energy transferred to or from the gas, if any, in the process in part (c)?

_______Heat is transferred to the gas._______Heat is transferred from the gas._______No heat is transferred in the process.Justify your answer.

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Isochoric ProcessHow to Identify them: Volume stays constant

Practice Problem: Isochoric expansion

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Figure 2- In an isochoric process, the pressure changes but the volume does not

Isothermal ProcessHow to Identify it: The isothermal process happens at a constant temperature. The pressure and

volume change, so work is done, but U is zero.

Adiabatic ProcessDefinition: In an adiabatic process, heat is neither added or taken away from the system.

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Figure 3-Isothermal processes follow the lines of the isotherm

Figure 4-Adiabatic Demo

Ways to create an Adiabatic Process1. The system can be insulated so that heat can neither enter nor leave. Example: Joule’s “heat equivalent” experiment was adiabatic

2. The other way to have an adiabatic process (this is actually called a “near adiabatic process”) is to have it happen very quickly. The process happens so fast that there is no time for heat to be transferred. Example: The combustion of gasoline in an engine is considered to be adiabatic because each combustion step happens in a

very short time – a few hundredths (or less) of a secondWhat Happens in an Adiabatic Process

1. A gas that is adiabatically expanded will lose internal energy (U ) and become cooler.2. A gas that is adiabatically compressed will gain U and become warmer.

Practice Problem: Adiabatic Expansion

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Figure 5- adiabatic process graphs look like isotherms but they are actually changing their temperature