AEROSPACE ENGINEERING

LAB 1

(MEC 2700)

LABORATORY

MANUAL

JULY 2007

Table of Contents

Experiment 1: Heat Capacity of Gases

Experiment 2: Thermal and Electrical Conductivity of Metals Experiment 3: Heat Pump

Experiment 4: Heat Conduction

Experiment 5: Free and Forced Convection

Experiment 6: Thermal Radiation

Experiment 1: Heat Capacity of Gases

1. BACKGROUND

The first law of thermodynamics can be illustrated particularly well with an ideal gas. This law describes the relationship between the change in internal intrinsic energy ΔUi the heat exchanged with the surroundings ΔQ and the constant-pressure change pdV.

dQ = dUi + pdV (1)

The molar heat capacity C of a substance results from the amount of absorbed heat and the temperature change per mole:

(2)

n = number of moles

One differentiates between the molar heat capacity at constant volume CV and the molar heat capacity at constant pressure Cp.

According to equations (1) and (2) and under isochoric conditions (V const., dV = 0), the following is true:

(3)

and under isobaric conditions (p = const., dp = 0):

(4)

Taking the equation of state for ideal gases into consideration:

pV = n R T (5)

it follows that the difference between Cp and CV for ideal gases is equal to the universal gas constant R.

Cp – CV = R (6)

It is obvious from equation (3) that the molar heat capacity CV is a function of the internal intrinsic energy of the gas. The internal energy can be calculated with the aid of the kinetic gas theory from the number of degrees of freedom f:

(7)

where

kB = 1.38 · 10-23 J/K (Boltzmann Constant)

NA = 6.02 · 1023 mol-1 (Avogadro's number)

Through substitution of

R = kB NA (8)

it follows that

(9)

and taking equation (6) into consideration:

(10)

The number of degrees of freedom of a molecule is a function of its structure. All particles have 3 degrees of translational freedom. Diatomic molecules have an additional two degrees of rotational freedom around the principal axes of inertia. Triatomic molecules have three degrees of rotational freedom. Air consists primarily of oxygen (approximately 20%) and nitrogen (circa 80%). As a first approximation, the following can be assumed to be true for air:

f = 5

CV = 2.5 R

CV = 20.8 J · K-1 · mol-1

and

Cp = 3.5 R

Cp = 29.1 J · K-1 · mol-1.

2. OBJECTIVE

The experiment aims to determine the molar heat capacities of air at constant volume Cv and at constant pressure Cp.

3. EQUIPMENT

Precision manometer

Barometer/Manometer

Digital counter

Digital multimeter

Aspirator bottle (10000 ml)

Gas syringe (100 ml)

Stopcock, 1-way and 3-way

Rubber stopper, d = 32/26 mm, 3 holes

Rubber stopper, d = 59.5/50.5 mm, 1 hole

Rubber tubing, d = 6 mm

Nickel electrode

Chrome-nickel wire

Push-button switch

4. PROCEDURE

Part A – Determining the Constant Value Cv

i) The setup is as shown in Figure 1.

ii) To determine Cv, connect the precision manometer to the bottle with a piece of tubing. The manometer should be positioned exactly horizontally. Pressure increase has to be read immediately after the heating process. iii) Begin the measuring procedure by pressing the push button switch. The measuring period should be less than a second. iv) Take readings of the pressure (from the manometer), the current and voltage. v) Remove the air from the aspirator bottle after each measurement. vi) Repeat steps iii) to v) in order to obtain 10 sets of results. Vary Δt within the given range.

Part B – Determining the Constant Value Cp

i) The setup is as shown in Figure 2.

ii) Replace the precision manometer with two...