Self-examination questions
1. Write down and explain ideal gas state equation.
2. Give the definitions of specific and molar heats and write down the relationship between them.
3. Formulate the first law of thermodynamics; apply it for adiabatic process and for processes at constant temperature, pressure, volume.
4. Write down Mayer’s equation and explain the essence of the gas constant R.
5. How is it possible to express molar heats at constant pressure and volume according to molecular theory?
6. What is the number of molecule freedom degrees?
7. Deduce the formula for an adiabatic exponent calculation.
8. Why is a Cp value always higher than a CV value?
9. Why does gas get cold as it increases in volume and on the contrary gets hot as it diminishes in volume?
Laboratory work 2.2 Determination of liquid internal friction (dynamic viscosity) coefficient
The purpose of the work: to study the transmission processes; experimental determination of the internal friction coefficient.
Theoretical information
In 1744, Lomonosov stated the principles of molecular theory and explained many phenomena from molecular-kinetic point of view. According to the theory, molecules of gas or liquid are carried from one place to another and change their velocities under some impacts. Thus, molecules take part in thermal motion.
M
olecules
impart their energy and momentum one to the other making more than
five milliard collisions with other molecules every second. It
promotes smoothing out inhomogeneities and leads to the processes
generally called transmission processes.
Alignment of temperatures in space is called heat conduction. Energy is transferred during heat conduction.
Immixture of different substances and mass transfer are called diffusion.
Transforming direct motion of the given layer of molecules into chaotic thermal motion is called internal friction or dynamic viscosity. The substance transfers momentum during internal friction because the fast layer molecules penetrate into the slower layer, bring larger momentum to the slow layer molecules, and speed the slow layer up. On the contrary, the fast layer slows down until speeds of all layers become the same.
The Newton’s law is applied to a steady laminar stream of a viscous liquid (see Fig. 6.2)
,
where
F
is a force of internal friction in the liquid or gas on area
S;
is
a coefficient of internal friction (dynamic viscosity);
is a velocity gradient of liquid stream in the direction
perpendicular to area
;
dv is a difference of velocities of two layers separated by dz distance.
Sign minus shows that the direction of force F and the direction of velocity gradient are opposite.
The coefficient of internal friction depends on a liquid type. The temperature of a liquid being raised, the coefficient decreases according to the exponential law:
,
where o is a coefficient independent of temperature;
k=1.38
– Boltzmann’s constant;
U is the energy of a molecule necessary to change its place.
There exists the general formula to determine the coefficient
,
where
v
is a mean velocity of the molecules; l
is a
mean
free path of the molecules;
is a density of the liquid.
There are many ways to determine the coefficient experimentally. Among them, the Stokes method is the most popular. It is based on the sped of a small ball dropped into a liquid.