Question

i) Evaluate the ratio ((1)/(/)bar (v^(2)))/(/)bar ((1)/(v^(2))) for a gas of molecules obeying Maxwell- Boltzmann statistics; v is the molecular speed. Hint: I=int_(-infty )^(infty ) e^(-ax^(2))dx=sqrt((pi )/(a)). ii) Show that if every state energy epsi _(s) in the partition function of a system is shifted by by a constant, say, epsi _(0), the mean value of the energy E is shifted by epsi _(0), but that its entropy remains unchanged. iii) State a precise criterion for the validity of the classical approximation. iv) The spectrum of a harmonic oscillator, in thermal contact with a heat reservoir, is given by E_(n)=(n+(1)/(2))ℏomega . Determine eta ℏomega so that the ratio of the probability the oscillator is in the E_(n+1) state over that in the E_(n) state is equal to (1)/(2). i) Evaluate the ratio (1/ v2) / 1/v2 for a gas of molecules obeying Maxwell- Boltzmann statistics; v is the molecular speed. Hint: I = D/2^=xp ii) Show that if every state energy ss in the partition function of a system is shifted by by a constant, say, &o, the mean value of the energy E is shifted by so, but that its entropy remains unchanged. iii) State a precise criterion for the validity of the classical approximation. iv) The spectrum of a harmonic oscillator, in thermal contact with a heat reservoir, is given by E, =(n+1/2)hw. Determine Bhw so that the ratio of the probability the oscillator is in the E,+ state over that in the E, state is equal to /.

          i) Evaluate the ratio ((1)/(/)bar (v^(2)))/(/)bar ((1)/(v^(2))) for a gas of molecules obeying Maxwell-
Boltzmann statistics; v is the molecular speed. Hint: I=int_(-infty )^(infty ) e^(-ax^(2))dx=sqrt((pi )/(a)).
ii) Show that if every state energy epsi _(s) in the partition function of a system is shifted by by
a constant, say, epsi _(0), the mean value of the energy E is shifted by epsi _(0), but that its entropy
remains unchanged.
iii) State a precise criterion for the validity of the classical approximation.
iv) The spectrum of a harmonic oscillator, in thermal contact with a heat reservoir, is
given by E_(n)=(n+(1)/(2))ℏomega . Determine eta ℏomega  so that the ratio of the probability the
oscillator is in the E_(n+1) state over that in the E_(n) state is equal to (1)/(2).
i) Evaluate the ratio (1/ v2) / 1/v2 for a gas of molecules obeying Maxwell-
Boltzmann statistics; v is the molecular speed. Hint: I =
D/2^=xp
ii) Show that if every state energy ss in the partition function of a system is shifted by by
a constant, say, &o, the mean value of the energy E is shifted by so, but that its entropy remains unchanged. iii) State a precise criterion for the validity of the classical approximation. iv) The spectrum of a harmonic oscillator, in thermal contact with a heat reservoir, is given by E, =(n+1/2)hw. Determine Bhw so that the ratio of the probability the
oscillator is in the E,+ state over that in the E, state is equal to /.

i evaluate the ratio 1bar v2bar 1v2 for a gas of molecules obeying maxwell boltzmann statistics v is the molecular speed hint iint infty infty e ax2dxsqrtpi a ii show that if every state en 90779

Added by Charles F.

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