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Physics
Concepts in Thermal Physics
104 SOLVED PROBLEMS
Question: 33.8
Show that eqn 33.103 holds for the problem considered in Example 33.5. ...
Verified Answer:
Recall from Example 33.7 that
\widetilde{C}...
Question: 35.1
What is the Jeans density of a cloud composed of hydrogen atoms and with total mass M⊙ at 10 K? ...
Verified Answer:
Using eqn 35.10,
ρ_{J} = \frac{3}{4πM^{2} }...
Question: 34.3
Derive an expression for κ in terms of the kinetic coefficients. ...
Verified Answer:
Substitution of eqn 34.45 into eqn 34.44 yields [l...
Question: 33.1
Find the solution to the equation of motion (known as the Langevin equation) for the velocity v of a particle of mass m which is given by mv = −αv + F(t), (33.1) where α is a damping constant (arising from friction), F(t) is a random force whose average value over a long time period, 〈F〉, is zero. ...
Verified Answer:
Note first that in the absence of the random force,...
Question: 33.7
Find the velocity autocorrelation for the Brownian motion particle governed by eqn 33.1 where the random force F(t) is as described in the previous example, i.e. with 〈F(t)F(t′)〉 = Aδ(t−t′). Hence relate the constant A to the temperature T. ...
Verified Answer:
Equation 33.1 states that
m\dot{v} = −αv + ...
Question: 33.6
A random force F(t) has average value given by 〈F(t)〉 = 0 (33.85) and its autocorrelation function is given by 〈F(t)F(t′)〉 = Aδ(t−t′), (33.86) where δ(t−t′) is a Dirac delta function.^9 Find the power spectrum. ...
Verified Answer:
By the Wiener–Khinchin theorem, the power spectrum...
Question: 33.5
Find the reponse function for the damped harmonic oscillator (mass m, spring constant k, damping α) whose equation of motion is given by mx + αx + kx = f (33.74) and show that eqn 33.73 holds. ...
Verified Answer:
Writing the resonant frequency
ω^{2} _{0} =...
Question: C.2
Find the ratio of the radius r to the height h of a cylinder which maximizes its total surface area subject to the constraint that its volume is constant. ...
Verified Answer:
The volume V = πr²h and area A = 2πrh + 2πr², so w...
Question: 37.1
How large a solar panel do you need to drive a television (which needs 100 W to run) on a sunny day, assuming that the solar panel operates at 15 % efficiciency? ...
Verified Answer:
Assuming that you have the full S = 1 .36 kW [late...
Question: 36.4
Above what mass will a neutron star become unstable? ...
Verified Answer:
The high gravitational fields and compact nature of...
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