Chapter 19

The First Law of Thermodynamics

Lecture by Dr. Hebin Li

PHY 2048, Dr. Hebin Li

Due at 11:59pm on Sunday, December 7

HW set on Masteringphysics.com

Assignment

Final exam:

Time: 2:15pm~4:15pm, Monday, December 8.

Location: Green Library 100

On all chapters

PHY 2048, Dr. Hebin Li

Physics II (spring 2015)

Physics with calculus II in spring 2015.

PHY 2049-(U02 ~ U07)

Lecture: Mondays 8:00 am ~ 9:40 am, AHC3-110

Recitation: Wednesdays 2:00 pm ~ 3:50 pm, locations vary

Textbook: University Physics (13th edition) by Sears &

Zemansky, Volume II (Chapter 21 ~ 36)

Masteringphysics will be needed for HW.

PHY 2048, Dr. Hebin Li

Goals for Chapter 19

To represent heat transfer and work done in a thermodynamic

process and to calculate work

To relate heat transfer, work done, and internal energy change

using the first law of thermodynamics

To distinguish between adiabatic, isochoric, isobaric, and

isothermal processes

To understand and use the molar heat capacities at constant

volume and constant pressure

To analyze adiabatic processes

PHY 2048, Dr. Hebin Li

Thermodynamics systems

A thermodynamic system is any

collection of objects that may

exchange energy with its

surroundings.

In a thermodynamic process, changes

occur in the state of the system.

Careful of signs! Q is positive when

heat flows into a system. W is the

work done by the system, so it is

positive for expansion.

PHY 2048, Dr. Hebin Li

Work done during volume changes

Microscopic picture:

Macroscopic picture:

The work done by the gas as the piston moves 𝑑𝑥

𝑑𝑊 = 𝐹𝑑𝑥 = 𝑝𝐴𝑑𝑥Since 𝑑𝑉 = 𝐴𝑑𝑥

Then 𝑑𝑊 = 𝑝𝑑𝑉

𝑊 = 𝑉1

𝑉2

𝑝𝑑𝑉

If the pressure is constant 𝑊 = 𝑝(𝑉2 − 𝑉1)

PHY 2048, Dr. Hebin Li

Work on a pV diagram

The work done equals the area under the curve on a pV-diagram.

Work is positive for expansion and negative for compression.

PHY 2048, Dr. Hebin Li

Work depends on the path chosen

When a thermodynamic system changes from an initial state to

a final state, it passes through a series of intermediate states.

This series of states is the path of the process.

The work done by the system depends not only on the initial

and final states, but also on the intermediate states, i.e. the path.

PHY 2048, Dr. Hebin Li

Internal Energy

The internal energy of a system is the

sum of the kinetic energies of all

particles in the system, plus the sum

of all the potential energies of

interaction among these particles.

It is not practical to calculate or

measure the absolute internal energy.

The change in internal energy

depends on the heat transfer and

work done

𝑈2 − 𝑈1 = ∆𝑈 = 𝑄 −𝑊

(First law of thermodynamics)

PHY 2048, Dr. Hebin Li

First Law of Thermodynamics

First law of thermodynamics: The change in the internal energy U of a system is equal to the heat added minus the work done by the system:

U = Q – W.

The first law of thermodynamics is just a generalization of the conservation of energy.

Both Q and W depend on the path chosen between states, but U is independent of the path.

If the changes are infinitesimal, we write the first law as

dU = dQ – dW.

PHY 2048, Dr. Hebin Li

Cyclic processes and isolated systems

• In a cyclic process, the system returns to its initial state. The internal energy change is zero. Then

𝑈2 = 𝑈1 and 𝑄 = 𝑊.

• A isolated system does no work and has no heat flow in or out. That is

𝑊 = 𝑄 = 0 and ∆𝑈 = 0

Heat transfer and work in the

process aba.

PHY 2048, Dr. Hebin Li

Four kinds of thermodynamics processes

Adiabatic: No heat is transferred into or out of the system, so Q = 0.

Isochoric: The volume remains constant, so W = 0.

Isobaric: The pressure remains constant, so W = p(V2 – V1).

Isothermal: The temperature remains constant.

PHY 2048, Dr. Hebin Li

Internal energy of an ideal gas

• The internal energy of an ideal gas depends only on its temperature, not on its pressure or volume.

• The temperature of an ideal gas does not change during a free expansion.

PHY 2048, Dr. Hebin Li

Heat capacities of an ideal gas

CV is the molar heat capacity at constant volume.

Cp is the molar heat capacity at constant pressure.

The figure at the right shows how we could measure the two molar heat capacities.

To produce the same temperature change, more heat is required at constant pressure than at constant volume. (∆𝑈 is the same)

𝐶𝑝 = 𝐶𝑉 + 𝑅