Molecular Physics | Thermodynamics Answers

Derive an expression for adiabatic lapse rate.

Establish Boltzmann's entropy relation.

Calculate van der Waals' constants for
helium using the data Tc = 5.3 K,
pc = 2.25 atm and R = 8.31 J morl K-1.

Starting from the equation of motion of a
linear harmonic oscillator, show that its
phase space is an ellipse.

Derive Clausius-Clapeyron equation for the
first-order phase transition.

A factory siren has a frequency of 990 Hz.
Calculate the frequency heard by a person
sitting in a car moving at 72 kmh-1 (i) away
from the siren and (ii) towards the siren.
Take the speed of sound in air as 330 ms-1.

The symmetry of (2,0,0) vibrational state of co2 is

A sonic depth gauge is placed 5.8 m above the ground. An ultrasound pulse sent downward reflects off snow and reaches the device 0.031 seconds after it was emitted. The air temperature is −20°C.

(a)
How far (in m) is the surface of the snow from the device? (Round your answer to at least three significant figures.)


(b)
How deep (in m) is the snow?

A baseball fan sitting in the "cheap seats" is
d = 156 m
from home plate (see the figure below).

How much time elapses between the instant the fan sees a batter hit the ball and the moment the fan hears the sound? (Assume the speed of sound is 344 m/s, and the vertical distance can be ignored.)

A person stands directly in front of two speakers that are emitting the same pure tone. The person then moves to one side until no sound is heard. At that point, the person is 4.90 m from one of the speakers and 4.95 m from the other. What is the frequency (in Hz) of the tone being emitted? (Assume air temperature to be 20°C.)