Physics

Thermodynamics

Thermodynamics

The study of heat and its transformation into mechanical energy is called thermodynamics.

Absolute zero is the temperature at which no more

energy can be extracted from a substance.

Absolute Zero

What are the limits of temperature?

• As thermal motion of atoms increases, temperature

increases.

• There seems to be no upper limit of temperature

• But there is a definite limit at the other end of the

temperature scale.

The absolute temperatures

of various objects and

phenomena.

Absolute Zero

Absolute Zero

A sample of hydrogen gas has a temperature of 0°C. If

the gas is heated until its molecules have doubled their

average kinetic energy (the gas has twice the absolute

temperature), what will be its temperature in degrees

Celsius?

What is a Thermodynamic System?

By system, we mean any group of atoms, molecules,

particles, or objects we wish to deal with.

• The system may be the steam in a steam engine,

• the whole Earth’s atmosphere,

• or even the body of a living creature.

It is important to define what is contained within the system

as well as what is outside of it.

Example of a Thermodynamic System

Consider a gas trapped in a

cylinder with a movable

piston.

Only the gas particles

constitute the system.

The cylinder and piston are

part of the environment. They

simply contain the gas in an

adjustable and measurable

volume.

Internal Energy

Internal Energy is the total energy of a system,

represented by U.

It would be impossible to determine U for a given system

– the complexity is enormous.

But we don’t have to!

Thermodynamics is only concerned with the change in

internal energy, ∆U.

Internal Energy in Thermodynamic Processes

1. INTERNAL ENERGY INCREASES – Energy is added

to the system and internal energy (as well as

temperature) increases. +∆U and +∆T

2. INTERNAL ENERGY DECREASES – Energy is

removed from the system, internal energy (and

temperature) decreases. -∆U and -∆T

3. ISOTHERMAL PROCESS – A thermodynamic process

where the temperature remains constant. Therefore,

∆U = 0 and ∆T = 0.

There are three possibilities for the value of internal energy

during any thermodynamic process:

Energy Transfer in Thermodynamics

1. WORK

2. HEAT

So how is energy transferred into or out of the system?

Isobaric Processes

ISOBARIC PROCESS: When the pressure remains

constant as the piston moves.

W = -P∆V

Work Done in Thermodynamic Processes

1. WORK IS DONE ON THE GAS – Pressure outside the

cylinder is greater than inside, piston moves inward.

a) Volume of gas is compressed: -∆V

b) The environment adds energy to the system, increasing

internal energy: +∆U

c) Work is done on the gas, so work is positive: +W

There are three possible outcomes which depend on how the

magnitudes of the pressures inside and outside the cylinder

compare to one another:

Work Done in Thermodynamic Processes

2. WORK IS DONE BY THE GAS – Pressure inside the

cylinder is greater than outside, piston moves outward.

a) Volume of gas expands: +∆V

b) The gas uses its energy to push the piston outward,

causing internal energy to decrease: -∆U

c) Work is done by the gas, so work is negative: -W

There are three possible outcomes which depend on how the

magnitudes of the pressures inside and outside the cylinder

compare to one another:

Work Done in Thermodynamic Processes

3. ISOMETRIC PROCESS – A thermodynamic process where

the volume of the gas remains constant. The pressure of the

environment outside the cylinder is the same as the pressure

of the gas inside the cylinder.

a) Net force is zero, so the piston doesn’t move.

b) ∆V = 0

c) No work is done, W = 0

There are three possible outcomes which depend on how the

magnitudes of the pressures inside and outside the cylinder

compare to one another:

Heat Reservoirs

• Recall that heat (Q) is transfer of thermal energy

between objects that have different temperatures.

• A heat reservoir is considered to be a source of

constant temperature in thermal contact with the system

and which will therefore transfer heat at a constant rate.

• We picture a “hot reservoir” as something from which we

can extract heat without cooling it down.

• Likewise we picture a “cold reservoir” as something that

can absorb heat without itself warming up.

Heat in Thermodynamic Processes

1. HEAT ADDED – When the heat reservoir has a higher

temperature (hot reservoir) than the gas inside the cylinder,

heat flows from the reservoir into the cylinder.

a) Heat added is considered positive, + Q

b) Internal energy increases, + ∆U

There are three possible outcomes for heat transfer depending on

the temperature of the heat reservoir as compared with the

temperature of the trapped gas in the cylinder:

Heat in Thermodynamic Processes

2. HEAT REMOVED – When the heat reservoir has a lower

temperature (cold reservoir) than the gas inside the cylinder,

heat flows out of the cylinder into the reservoir.

a) Heat removed is considered negative, - Q

b) Internal energy decreases, - ∆U

There are three possible outcomes for heat transfer depending on

the temperature of the heat reservoir as compared with the

temperature of the trapped gas in the cylinder:

Heat in Thermodynamic Processes

3. ADIABATIC PROCESS– A thermodynamic process where

no heat is added or removed. This occurs when the heat

reservoir and the trapped gas are in thermal equilibrium so

no heat can flow.

a) No heat is added or removed, Q = 0

There are three possible outcomes for heat transfer depending on

the temperature of the heat reservoir as compared with the

temperature of the trapped gas in the cylinder:

Energy Transfer in Thermodynamics

1. WORK

2. HEAT

So how is energy transferred into or out of the system?

± ∆U

+ W

- W

+ Q

- Q

First Law of Thermodynamics

For a system where internal energy is composed of only

thermal energy, the change in internal energy of the

system is equal to the energy transferred into or out of

the system by work and heat.

∆𝑈 = 𝑄 +𝑊

Let’s say you put an air-filled, rigid, airtight

can on a hotplate and add a certain amount

of energy to the can.

The can has a fixed volume and the walls of

the can don’t move, so no work is done.

All of the heat going into the can increases

the internal energy of the enclosed air, so its

temperature rises.

Isometric Process Example

Now, replace the can with a balloon.

As the air is heated it expands, exerting a force

for some distance on the surrounding atmosphere.

Some of the heat added goes into doing work, so less of the

added heat goes into increasing the enclosed air’s internal

energy.

The temperature of the enclosed air will be lower than that of

the air in the closed can.

Thermodynamics Example

When a gas is compressed or expanded so that no

heat enters or leaves a system, the process is said to

be adiabatic.

Adiabatic changes of volume can be achieved by:

• Performing the process rapidly so that heat has little

time to enter or leave.

• Thermally insulating a system from its surroundings.

Adiabatic Processes

Do work on a pump

by pressing down on

the piston and the air

is warmed.

Adiabatic Processes Example

One cycle of a four-stroke internal combustion engine.

Four-Stroke Internal Combustion Engine

One cycle of a four-stroke internal combustion engine.

Four-Stroke Internal Combustion Engine

One cycle of a four-stroke internal combustion engine.

Four-Stroke Internal Combustion Engine

One cycle of a four-stroke internal combustion engine.

Four-Stroke Internal Combustion Engine

One cycle of a four-stroke internal combustion engine.

Four-Stroke Internal Combustion Engine

Problem

During a thermodynamic process, 200 joules of heat are

added to a gas while 300 joules of work are done by the

gas. Determine the change in internal energy.

Problem

A. During an isothermal process, 1,000 joules of heat

are removed from a trapped gas. Determine the

change in internal energy of the gas.

B. Determine the work done on or by the gas.

C. Is this work done on the gas or by the gas?

Problem

During a thermodynamic process, 2,400 joules of heat

are removed from a gas while 600 joules of work are

done by the gas. Determine the change in internal

energy.

Problem

A gas trapped in a cylinder with a movable piston undergoes an

adiabatic process. During this process, the gas does 1,200 joules of

work. Which of the following statements is true?

A. The change in internal energy is zero.

B. The internal energy of the system increases by 1,200 joules.

C. The temperature of the gas remains unchanged.

D. The temperature of the gas increases.

E. The heat transferred into or out of the system is zero.

Problem

During an isothermal process, 600 joules of heat are

removed from a trapped gas. Determine the work done

on or by the gas and the change in internal energy of the

system.

Second Law of Thermodynamics

The second law of thermodynamics states that

heat will never, of itself, flow from a cold object

to a hot object.

Heat Engines

• A heat engine is any device that changes internal

energy into mechanical work.

• According to the second law of thermodynamics, no

heat engine can convert all heat input to mechanical

energy output.

When heat energy flows in any

heat engine from a hot

reservoir to a cold reservoir,

part of this energy is

transformed into work output.

Heat Engines

The second law states that when work is done by a heat

engine running between two temperatures, Thot and Tcold,

only some of the input heat at Thot can be converted to

work.

The rest is expelled as heat at Tcold.

Heat Engines

There is always heat exhaust, which may be desirable

or undesirable.

Hot steam expelled in a laundry on a cold winter day

may be quite desirable.

The same steam on a hot summer day is something

else. When expelled heat is undesirable, we call it

thermal pollution.

Heat Engines

The Carnot efficiency, or ideal efficiency, of a heat

engine is the ideal maximum percentage of input

energy that the engine can convert to work.

Thot is the temperature of the hot reservoir.

Tcold is the temperature of the cold reservoir.

Ideal Efficiency of Heat Engines

The actual efficiency of a heat engine is the ratio of

the total net work produced by the engine to the heat

added:

Actual Efficiency of Heat Engines

𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =𝑊𝑛𝑒𝑡

𝑄𝐻

Steam Turbine

A steam turbine engine demonstrates the role of

temperature difference between heat reservoir and sink.

Carnot’s equation states the upper limit of efficiency for all

heat engines.

The higher the operating temperature (compared with

exhaust temperature) of any heat engine, the higher the

efficiency.

Only some of the heat input can be converted to work—

even without considering friction.

Heat Engines

Problems

What is the ideal efficiency of an engine if both its hot

reservoir and exhaust are the same temperature—say,

400 K?

Problems

An engine operates between 27 degrees Celsius and

127 degrees Celsius. Determine its theoretical

efficiency.

Problems

A heat engine absorbs 2500 Joules of heat and exhausts

1500 J to a cold reservoir. What is the efficiency of this

engine?

The idea of entropy proceeds from the second law of

thermodynamics.

Natural systems tend to proceed from a state of order to a

state of greater disorder.

Another way to say this is that organized, usable energy

degenerates into disorganized, nonusable energy.

It is then unavailable for doing the same work again.

Entropy

Entropy

Entropy is the measure of the amount of disorder in a system.

Disorder increases; entropy increases.

Entropy

• The entropy of an isolated system cannot

decrease.

• The entropy of isolated systems always increases

until the system reaches equilibrium.

• Once at equilibrium, the entropy of the system

remains constant.

Entropy