Question
In: Physics
The probability that a gas molecule has the reduced kinetic energy, κ=(εkinetic/kT), is p(κ)=κ exp(–κ). (a)...
The probability that a gas molecule has the reduced kinetic energy, κ=(εkinetic/kT), is p(κ)=κ exp(–κ).
(a) Show that this probability distribution is properly normalized.
(b) Sketch a qualitative graph of the probability distribution vs. κ.
(c) Use integral calculus to determine the mean (average value) of κ.
(d) Use differential calculus to determine the mode (most common value)
of κ.
(e) Explain what qualitative feature of the distribution makes the mean greater than the mode.
Solutions
Expert Solution
Since the probability
distribution function is zero for k tends to infinite and at k=0,
this property make mean greater then mode
genius_generous answered 2 years agoRelated Solutions
If it has enough kinetic energy, a molecule at the surface of the Earth can escape...
If it has enough kinetic energy, a molecule at the surface of
the Earth can escape the Earth’s gravitation.
The acceleration of gravity is 9.8 m/s2, and the Boltzmanns’
constant is 1.38066 × 10−23 J/K.
minimum kinetic energy needed to escape in terms of the mass of
the molecule m, the free-fall acceleration at the surface g, and
the radius of the Earth R.
1. Kmin = 1 m g R 3
2. Kmin = 1mgR 2
3. Kmin...
Calculate the momentum p, kinetic energy K, and total energy E of an electron traveling at...
Calculate the momentum p, kinetic energy K,
and total energy E of an electron traveling at each of the
speeds tabulated below.
v
p (keV/c)
K (keV)
E (keV)
(a) 0.03c
(b) 0.4c
(c) 0.9c
The average kinetic energy of the molecules in a gas sample depends only on the temperature,...
The average kinetic energy of the molecules in a gas sample
depends only on the temperature, T. But given the same kinetic
energies, a lighter molecule will move faster than a heavier
molecule. Where R=8.314 J/(mol·K) and ℳ is molar mass in kilograms
per mole. Note that a joule is the same as a kg·m2/s2.
What is the rms speed of O2 molecules at 429 K?
What is the rms speed of He atoms at 429 K?
Glycine is an...
The average kinetic energy of the molecules in a gas sample depends only on the temperature,...
The average kinetic energy of the molecules in a gas sample
depends only on the temperature, T. But given the same kinetic
energies, a lighter molecule will move faster than a heavier
molecule. What is the rms speed of Cl2 molecules at 347 K? What is
the rms speed of He atoms at 347 K?
A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have...
A bicycle has a kinetic energy of 124 J. What kinetic energy
would the bicycle have if it had … Show how you got your answer on
your pdf copy. … twice the mass and was moving at the same speed? …
one-half the mass and was moving with twice the speed? … three
times the mass and was moving with one-half the speed? … the same
mass and was moving with one-half the speed? … the same mass and...
1) An electron has a kinetic energy that is 50% larger than its classical kinetic energy....
1) An electron has a kinetic energy that is 50% larger than its
classical kinetic energy. Electron mass is 0.511 MeV/c^2.
a. What is the speed of the electron expressed in the unit of
speed of light c?
b. What is the total energy of the electron expressed in the
unit of MeV?
c. What is the kinetic energy of the electron expressed in the
unit of MeV?
4. (a) Derive an integral expression for the probability of a gas molecule of mass m,...
4.
(a) Derive an integral expression for the probability of a gas
molecule of mass m, at temperature T is moving
faster than a certain speed vmin.
(b) A particle in the atmosphere near the earth’s surface
traveling faster than 11 km/s has enough kinetic energy to escape
from the earth’s gravitational pull. Therefore, molecules in the
upper atmosphere will escape if they do not have collisions on the
way out. The temperature of the upper atmosphere is about 1000K....
Which of these increases the average kinetic energy of the molecules in an ideal gas? (a) Reducing the volume, keeping P and N constant (b) Increasing the volume, keeping P and N constant
Which of these increases the average kinetic energy of the molecules in an ideal gas? (a) Reducing the volume, keeping P and N constant (b) Increasing the volume, keeping P and N constant (c) Reducing the volume, keeping T and N constant (d) Increasing the pressure, keeping T and V constant (e) Increasing N, keeping V and T constant
1. What is the momentum (p) of a 960-MeV proton (that is, its kinetic energy is...
1. What is the momentum (p) of a 960-MeV proton
(that is, its kinetic energy is 960 MeVMeV )?
Express your answer with the appropriate units.
2. An electron (mmm = 9.11×10−31 kg
) is accelerated from rest to speed vv by a conservative force. In
this process, its potential energy decreases by
6.70×10−14 JJ . Determine the electron's speed, v. (in
term of c.)
How is energy an eigenvalue? Do the math. Kinetic energy= T= 1/2 mv^2 = p^2 /...
How is energy an eigenvalue? Do the math.
Kinetic energy= T= 1/2 mv^2 = p^2 / 2m = h^2 / 2m Lambda^2
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Design a Moore sequential circuit that has an input X and an output Y. The circuit...
- Both AgCl and AgI are very sparingly soluble salts, but the solubility of AgI is much...
- Write assembly programs with the following I/O Enter a sentence: Project No Three. No. of uppercase...
- 1. Many operating systems now operate on 64 bits of memory. What is the highest base...
- 1. The empirical rule says that 95% of the population is within 2 standard deviations of...
- What are some adaptive traits for tigers what are some adaptations of a tiger
- Question I'm having trouble with: Using LISP, write a recursive function that takes a list and...
ADVERTISEMENT