The First Law of Thermodynamics

The Law of Conservation of Energy

The First Law of Thermodynamics

You already know this!!!! Energy cannot be created nor destroyed. The total energy of the universe is constant. As an equation this is:

KE PE U Q W∆U is the change in internal energy of the systemQ is the amount of heat transferred to or from the systemW is the amount of mechanical work done on the system.

The First Law of Thermodynamics

∆KE and ∆PE refer to the system as a whole Basically they matter if the object is moving or at a height above a zero

point. For most thermodynamics problems, this isn’t the case and ∆KE =

∆PE = 0. Then our equation reduces to:

U Q W

Kinetic Theory

• We know that the molecules that make up matter are in a constant state of motion.

• Solids – the molecules are fixed in position & vibrate.• Liquids – the molecules are bound to other molecules

and are free to move over each other.• Gases – the molecules are free to move.• Ideal Gas – There are many molecules, the molecules

are very far apart, the molecules only interact when they collide and the collisions are elastic (momentum & kinetic energy are conserved).

Kinetic Theory for Ideal Gases• Since the molecules of an ideal gas are moving, each

molecule has kinetic energy.• The average kinetic energy of all the molecules in an

ideal gas are directly proportional to the temperature of the ideal gas.

Kinetic Theory for Ideal Gases• We can also define the average kinetic energy of the

molecules in an ideal gas in terms of a kind of “average” speed of the molecules: the root-mean-square speed (vrms)

• The root-mean-square speed is the most probable speed of the molecules in a gas.

Internal Energy The sum total of all the energy of all the

molecules in an object. Very much related to the temperature of a

substance. The internal energy of an ideal gas is the

total kinetic energy of all of the molecules in the gas.

Internal Energy of an Ideal GasIn terms of the number of molecules (N) and

Boltzmann’s Constant:

UNKEavg N( 32 kBT) 3

2 NkBTIn terms of the number of moles of the gas

(n) and the Universal Gas Constant:

Internal Energy of an Ideal Gas

In terms of the number of molecules (N) and Boltzmann’s Constant:

TNkU B23

TnRU 23

In terms of the number of moles of the gas (n) and the Universal Gas Constant:

Heat Transfer

The transfer of energy from one object to another BECAUSE of difference in temperature.

Heat always flows from high temperature to low temperature.

Heat was measured in calories (cal) A calorie is the amount of heat necessary

to raise the temperature of 1 gram of water 1oC.

Heat Transfer

In the 1800’s James Prescott Joule performed an experiment that showed heat and energy are related.

This was called the mechanical equivalent of heat.

Basically Joule found that 4.186-J = 1 cal. We will use Joules for our unit of heat

transfer.

Heat Transfer

When heat is added to a system, Q > 0. When heat is removed from a system, Q <

0. Heat is transferred in three ways: Conduction - When two or more objects

are in physical contact with each other and heat flows from one object to another.

Conduction is carried out by the collision of particles at the boundaries of the objects transferring kinetic energy.

Heat Transfer

Convection - When heat flows through the mass movement of molecules from one place to another.

When air near the Earth’s surface is heated by the ground it rises. When this air rises it cools and then sinks again. These are called convection currents.

Radiation - Substances absorb light, microwaves, Ultraviolet Rays, x-rays, radio waves or gamma rays. This excites the molecules in the substance causing them to vibrate or move faster, increasing the average kinetic energy of the substance.

The First Law of Thermodynamics

U Q W

• In an isobaric process the pressure remains constant.• In this case we can use W = -P∆V.• In this case our equation for the First Law of

Thermodynamics becomes:

∆U = Q - P∆V

• The ideal gas law in this case reduces to:𝐕𝟏𝐓𝟏 = 𝐕𝟐𝐓𝟐

• In an isothermal process the temperature remains constant.• This means ∆T = 0 and more importantly ∆U = 0.• In this case our equation for the First Law of Thermodynamics

becomes:

0 = Q + W or Q = -W

• The ideal gas law in this case reduces to:

P1V1 = P2V2

An Adiabatic ProcessAn Adiabatic Process

• In an adiabatic process there is no heat transfer.

• This means Q = 0.

• In this case our equation for the First Law of Thermodynamics becomes:

∆U = W

• The ideal gas law in this case reduces to:

𝐏𝟏𝐕𝟏𝐓𝟏 = 𝐏𝟐𝐕𝟐𝐓𝟐

In an isovolumetric process the volume of the gas stays constant.This means W = 0.In this case our equation for the First Law of Thermodynamics becomes:

∆U = QThe ideal gas law in this case reduces to:

An Isovolumetric ProcessAn Isovolumetric Process

𝐏𝟏𝐓𝟏 = 𝐏𝟐𝐓𝟐