Problems and Solutions on Thermodynamics and Statistical Mechanics

348 Problems €4 Sdutiom on Thermcdylam'cs 8 Statistical Mechanics

Assuming v(0) = 0, we have

u(t) = ~(s) exp[(s - t),O]ds ,

l

where t > 0, ,O = r/m, F(t) = f(t)/m. Consider

1, x>o,

0. x<o.

where, 6(x) =

..

kT

m

a = 2PmkT = 27kT.

At thermal equilibrium, (u2(t)) = -.

result gives

Comparing this with the above

Next, consider

t

Ax = x(t) - z(0) = 1 u(s)ds ,

and