In: Physics

The average thermal energy of a particle is ~ k_{B}T
where k_{B} is Boltzmann’s constant and T is the
temperature in degrees Kelvin. At room temperature, k_{B}T
= 25 meV = 4.1 x 10-21 J = 4.1 pN – nm =0.6 kcal/mole (eV =
electron volts; J = Joules, N = Newtons; kcal = kilocalories).

a. A typical molecular motor uses 100 to 1000 ATP molecules per second. Calculate how much energy is dissipated in the motor (in Watts, or J/s). Call this power quantity M.

b. Nuclear vibrations occur on the time scale of
10^{-13} sec. Compute the scale of power input to a
molecular motor from random collisions with surrounding water and
call it R, assuming that the collisions transfer about
k_{B}T of energy each. Estimate the ratio R/M.

c. How does your estimate differ if you assume that water
molecules require a diffusion time given by Δx^{2}/D to
transfer k_{B}T of energy to the motor, where Δx is the
average distance between water molecules in solution?

The kinetic energy of a particle is equal to the energy of a
photon. The particle moves at 6.1% of the speed of light. Find the
ratio of the photon wavelength to the de Broglie wavelength of the
particle. Take the speed to be non-relativistic.

A particle moves in the xy plane with constant acceleration. At
t = 0 the particle is at vector r1 = (3.6 m)i + (2.8 m)j, with
velocity vector v1. At t = 3 s, the particle has moved to vector r2
= (11 m)i − (1.8 m)j and its velocity has changed to vector v2 =
(4.6 m/s)i − (6.7 m/s)j. (a) Find vector v1. vector v1 = m/s
(b) What is the acceleration of the particle? vector a...

A particle moves in the xy plane with constant
acceleration. At t = 0 the particle is at r1 =
(4.0 m) + (3.0 m), with velocity 1. At t = 3 s,
the particle has moved to r2 = (9 m) − (2.0 m) and its
velocity has changed to v2 = (5.0 m/s) − (6.0 m/s).
i. Find 1 = m/s
ii. What is the acceleration of the particle?
iii. What is the velocity of the particle as...

Net-Ionic Equation for Hydrolysis? Expression for equilibrium
constant (Ka or Kb)? Value of Ka or Kb? for NaC2H3O3, Na2CO3,
NH4Cl, ZnCl2, KAl(SO4)2

Overall, 80% of the energy used by the body must be eliminated
as excess thermal energy and needs to be dissipated. The mechanisms
of elimination are radiation, evaporation of sweat (2,430 kJ/kg),
evaporation from the lungs (38 kJ/h), conduction, and
convection.
A person working out in a gym has a metabolic rate of 2,500 kJ/h.
His body temperature is 37°C, and the outside temperature 20°C.
Assume the skin has an area of 2.0 m2 and emissivity of
0.97. (σ =...

What is the equation for the thermal time constant? What is the
physical significance of the thermal time constant? Can you
determine the validity of lumped capacitance from the thermal time
constant if given the Fourier number?

In a high-energy collision between a cosmic-ray particle and a
particle near the top of Earth's atmosphere, 104 km above sea
level, a pion is created.The pion has a total energy E of 1.92 ×
105 MeV and is traveling vertically downward. In the
pion's rest frame, the pion decays 35.0 ns after its creation. At
what altitude above sea level, as measured from Earth's reference
frame, does the decay occur? The rest energy of a pion is 139.6
MeV.

A system for the storage of thermal energy is to be designed
using an underground tank of water. The tank is buried at a depth
of 3 m and is a cube of 1 m on each side. The water in the tank is
heated by circulating it through a solar energy collection system.
A given heat input to the water may be assumed due to the solar
energy flux. Characterize the design problem in terms of
the fixed quantities...

What is Plank’s constant and the significance of this constant?
A ray having an energy of 12 eV is required to create an electrical
current in a circuit when the ray is shone on a piece of metal in
the circuit. Determine the frequency of this ray. What is this
called and what major revelation resulted from this type of
experiment

Identify the forms of energy based on each example: Nuclear,
Mechanical, Light, Heat, Thermal, chemical energy.
The energy released when two polymers are hydrolyzed.
Separation of positive and negative charges across a membrane
drives the movement of ions through channels.
Energy transfer due to a temperature difference.
Photons hit the eye and are interpreted as images Muscles
contract allowing for skeletal movement.
A radioisotope decays, releasing large amounts of energy.

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