GATE CY 2015 Question Paper (31-Jan-2015) (Shift 1)

The rotational partition function of a diatomic molecule with energy levels corresponding to J = 0 and 1, is (where, $ϵ$ is a constant)

The internal energy of an ideal gas follows the equation $U=3.5PV+k$, where k is a constant. The gas expands from an initial volume of $0.25m^3$ to a final volume of $0.86m^3$. If the initial pressure is $5N{m}^{-2}$, the change in internal energy (in Joules) is (given $P{V}^{1.3}$ = constant) ________

The solubility product of AgBr(s) is $5\times 10^{-13}$ at 298 K. If the standard reduction potential of the half-cell, $E_{Ag|AgBr(s)|B{r}^{-}}^0$ is 0.07 V, the standard reduction potential, $E_{A{g}^{+}|Ag}^0$ (in volts) is ________

One mole of a substance is heated from 300 K to 400 K at constant pressure. The $C_p$ of the substance is given by, $C_p$ (J $K^{-1}mo{l}^{-1}$) = $5+0.1T$. The change in entropy, in J $K^{-1}mo{l}^{-1}$, of the substance is ________

The potential energy (PE) versus reaction coordinate diagrams for electron transfer reactions with rate constants $k_1$, $k_2$ and $k_3$, are given below. The increasing order of the rate constants is