writing a lab report for physical chemistry lab. " speed of sound in different gases"

I. Organization/syllabus .

CHM 343 Lecture 1 Fall 18

Chemistry 343(#70601): Fall 2018

I. Organization/syllabus (cont.).

6 experiments:

There will be a 25%/week of 60 point penalty late reports

Record Data

Take Quiz

1st lab session

(group effort)

Analyze Data

2nd lab session

(group effort)

Write report

(individual effort)

3rd lab session

(group effort)

Record Data

Take Quiz

Turn in report

Via Blackboard

Absent

-20 pts

Absent

-20 pts Perfect written report

 +60 pts

Procedure:

I. Organization/syllabus (cont.).

Use the Posted grading Rubric (on Blackboard) as a guide.

From Blackboard for Exp. #1 speed of sound (SoS).

Policy at ASU

Schedule details are in syllabus

Schedule details are in syllabus (cont.)

The Speed of Sound

When aircraft get to between 25,000 –

30,000 ft, they reference their speed to a

“Mach Number”. This is simply a percentage

of the speed of sound. For example, a Mach

Number of 0.80 is 80% of the speed of

sound. This is not a fixed speed, as the

speed of sound varies with the temperature

of the air.

When aircraft approach the speed of sound,

shockwaves start to form which causes

aerodynamic issues. Aircraft therefore have

a maximum mach number they can fly at,

which is why this becomes the reference

speed.

II. Experiment 1: Speed of sound

How Fast Do Airliners Fly?

Goal: measure the speed of sound in He, N2 at room temperature and CO2 at various temperature

Standing wave with wavelength l, freq, n

II. Heat Capacity Ratio- Introduction

Approach described in text: use fixed frequency and measure wavelength

The “modernized” approach for measuring the speed of sound.

L=length Described in “Heat

Cap._inter” document

found on Blackboard

1)

II. Experiment 1: Speed of sound Heat Capacity Ratio- Introduction

(Exp. # 3 in Text)

Goal: measure the speed of sound in He, N2 and CO2 and relate this data to Heat Capacity ratio, 

2)

Heat capacity at constant pressure

Heat capacity at constant volume

  CP/ Cv = Mc 2/RT

If the gas is assumed to be “Ideal” it can be shown

Speed of sound

Mass

c2=RT/M

For an van der Waals gas it can be shown that:

c2 3) c=speed of sound

Definition heat capacity ratio:

Eqs. 2 & 3 are what we will use to relate our measurements (i.e. c) to 

Note for a perfect gas : Cp  Cv +R 4)

 experiment  c + Eq.4  Cv( experiment)

We also want Cv( theory)

II. Heat Capacity Ratio- Introduction

Theoretical value for

Cv via “Equipartition

Theorem” and

“Statistical Mechanic”

Experimental value

for Cv via Speed of

Sound (SoS) and

associated error

estimate

Heat capacities, E, Rotations, vibrations

Two theories: 1) Equipartiton Theorem; 2) Statistical Thermodynamics

Relating data (heat capacities) to properties of atoms and molecules

Equipartition theorem: “ Each term in the classical expression for the atomic or molecular energy, E, that is quadratic in the coordinate or a momentum contributes RT/2 to the thermodynamic average energy, U, and thus R/2 to Cv”

II. Heat Capacity Ratio- Introduction (cont.)

experiment   + Eq.4  Cv( experimental) Would like to also get Cv( Theory)

Equipartition theorem is a classical mechanics idea and is only applicable when the energy levels are approximately expressed using classical mechanics. Vibrational energy levels are widely spaced and we must use a more correct expression derived from Statistical Mechanics

The heat capacity ratio, , enters into the description of numerous physical phenomena. Consider the expansion of a gas through a small orifice:

Supersonic expansions: a use of 

High-pressure region Low-pressure region

Properties (Temperature, T, Velocity, V, collision frequency n,

density, n, as a function of distance from nozzle)

Note: all properties are described in terms of use of  Cp/Cv

Center line

Distance from orifice/diameter of orifice

II. Heat Capacity Ratio- Introduction (cont.)

Temp.→

Velocity.→

Pressure →

Density →

Mach Disc

Examples: Rocket propulsion

Rocket man

III. Assignment (see Syllabus)

No Lab this week.

All Labs start Week Aug/28

There will be a quiz at the beginning of the lab

Turn in your contract to your TA.