Which of the following statement(s) is(are) correct regarding the root mean square speed (U_rms) and average translational kinetic energy (E_av) of a molecule in a gas at equilibrium?

For a reaction, $$A\,\,\rightleftharpoons\,\,P,$$ the plots of $$\left[ A \right]$$ and $$\left[ P \right]$$ with time at temperature $${T_1}$$ and $${T_2}$$ are given below.


If $${T_2} > {T_1},$$ the correct statement(s) is (are) (Assume $$\Delta {H^ \circ }$$ and $$\Delta {S^ \circ }$$ are independent of temperature and ratio of $$lnK$$ at $${T_1}$$ to $$lnK$$ at $${T_2}$$ is greater than $${{{T_2}} \over {{T_1}}}.$$ Here $$H,$$ $$S,G$$ and $$K$$ are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

A reversible cyclic process for an ideal gas is shown below. Here, $$P, V,$$ and $$T$$ are pressure, volume and temperature, respectively. The thermodynamic parameters $$q,w, H$$ and $$U$$ are heat, work, enthalpy and internal energy, respectively.



The correct option(s) is (are)

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $$K$$ in terms of change in entropy is described by