Teaching MPPSC Assistant Professor Mock Test Series 2025 Physical Sciences Thermodynamic and Statistical Physics
The system has two normal modes of vibrations with frequencies \(\omega_1 \) and \(\omega_2 = 2 \omega_1 \). What is the probability that at temperature T, the system has an energy less than \(4 \hbar \omega_1 \)? Let \(x= e^{-\beta \hbar \omega_1 } \) and Z be the partition function.
1
\(\rho = \frac{1}{Z} x^{1/2} \left[ 1+ 2 x + x^2 \right] \)
2
\(\rho = \frac{1}{Z} x^{1/2} \left[ 1+ x + 2 x^2 \right] \)
3
\(\rho = \frac{1}{Z} x^{3/2} \left[ 1+ x + 2 x^2 \right] \)
4
\(\rho = \frac{1}{Z} x^{5/2} \left[ 1+ x + 2 x^2 \right] \)