GATE CY 2019 Question Paper (02-Feb-2019) (Shift 1)

The entropy change for the melting of ‘x’ moles of ice (heat of fusion is 80 cal g⁻¹) at 273 K and 1 atm pressure is 28.80 cal K⁻¹. The value of ‘x’ is _________. (Round off to two decimal places)

(Molecular weight of water =18 g/mol)

Consider a two-state system at thermal equilibrium having energies 0 and 2k${}_B$ T for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is _______. (Round off to two decimal places)

(k${}_B$ is the Boltzmann constant)

Consider a system of three identical and distinguishable non-interacting particles and three available nondegenerate single particle energy levels having energies 0, ¢ and 2ε. The system is in contact with a heat bath of temperature T K. A total energy of 2ε is shared by these three particles. The number of ways the particles can be distributed is _______.

In a 400 MHz ¹H NMR spectrometer, a proton resonates at 1560 Hz higher than that of tetramethylsilane. The chemical shift value of this proton is _______ ppm. (Round off to one decimal place)

(Chemical shift of tetramethylsilane is fixed at zero ppm)

Gas phase bond length and dipole moment of a compound (MX) is 3 Å and 10.8 D, respectively. The ionic character in gas phase MX is _______%. (Round off to one decimal place)

(1D = 3.336 x 10⁻³⁰ Cm)