Thermodynamics

Thermodynamics States About Energy Conversion Thermodynamics is the branch of science that embodies the principles of energy transformation in macroscopic systems. The general restrictions which experience has shown to apply to all such transformations are known as the laws of thermodynamics. These laws are primitive; they cannot be derived from anything more basic. The first law of thermodynamics states that energy is conserved; that, although it can be altered in form and transferred from one place to another, the total quantity remains constant. Thus, the first law of thermodynamics depends on the concept of energy; but, conversely, energy is an essential thermodynamic function because it allows the first law to be formulated. This coupling is characteristic of the primitive concepts of thermodynamics. The words system and surroundings are similarly coupled. A system is taken to be any object, any quantity of matter, any region, and so on, selected for study and set apart (men

Wave Problem Solving

Problem 1.
A saxophone is playing a steady note of frequency 266 Hz. The temperature in the room is 25 oC. suppose that at some instant the varying pressure at your eardrum is at a maximum. How far away in meters is the next pressure maximum?

Solution:
The distance between the pressure maxima is an integer number of wavelength. Therefore the shortest distance is the wavelength. The speed of sound at 25 C is 346.33 m/s. Then we can find the wavelength:

L = v/f = 346.34/266 = 1.3 m

Problem 2.
(Inquiry into Physics-5th ed. Ostdiek,Bord) The quartz crystal used in an electric watch vibrates with frequency 32,768 Hz. What is the period of the crystals motion?

Solution:
By definition the frequency is the inverse period. Then the period is

 ζ = 1/f = 1/32768 = 3.05 x 10-5 s = 30.5 μs

Problem 3.
A sound wave traveling at 350 m/s has a frequency of 500 Hz. What is its wavelength?

Solution:
The wavelength is related to the frequency and the speed by the following relation.

λ = vT = v/f = 350/500 = 0.7 m

Problem 4.
Estimate how far away a cicada can be heard if the lowest possible audible intensity of a sound it produces is 5 x 10-10 W/m2 and the power of the cicada's sound source is. 4 x 10-6 W

Solution:
We can estimate that the total power of the cicada's sound is distributed uniformly over the spherical surface of radius R. Then at distance R the intensity of the sound is

I = 4 x 10-6/4πR2

The largest radius is achieved when the intensity is I = 5 x 10-10 W/m2 . Then

R2= 4 x 10-6/4π x 10-10 = 637 m2

Then R = 25 m

Problem 5.
Light of wavelength 497.0 nm appers to have a wavelength of 500.2 nm when it reaches eart from a distance star. find the velocity of the star if the speed of light is 300,000,000 m/s.

Solution:
In this problem we need to use the expression for the Doppler shift of the frequency of the wave for an observer moving relative to the source of the waves.. If the source of the light (wave) is moving with a speed v then the change in the frequency is

Δf = v/c x fo
where c = 3 x 108 m/s is the speed of light. Since

f = c/λ

Then
Δf  = Δ c/λ = c Δλ/λ2
and

From this expression we can find the speed of the source

v = c Δλ/λ = 3 x 108 x (500.2 - 497) x 10-9/(497 x 10-9 = 2 x 106 m/s