GATE CY 2016 Question Paper (31-Jan-2016) (Shift 2)

Consider a two-state system at thermal equilibrium with equal degeneracy where the excited state is higher in energy than the ground state by $0.1$ eV. The ratio of the population of the excited state to that of the ground state, at a temperature for which $k_{B}T=0.05$ eV, is ________

Of the vibrational modes given below, the IR active mode(s) is(are)

A system is described by the following real wavefunction.



The probability (P) of finding the particle in a region dx around points I, II, and III in the figure obeys the trend

The temperature-composition (T-x) phase diagram of the two-component system made of X and Y is given below. At a temperature of $288$ K and starting at the point P, Y is added until the composition reaches S. Which of the following statements is NOT TRUE?

For a system subjected to only P-V work, entropy is given by

1. $-(\frac{\partial G}{\partial T}{)}_P$
2. $-(\frac{\partial G}{\partial P}{)}_T$
3. $-(\frac{\partial A}{\partial V}{)}_T$
4. $-(\frac{\partial A}{\partial T}{)}_V$