Mix Examples- States of Matter Questions in English

(C) According to Newton's law of viscosity,the viscous force $(F)$ acting between two layers of a liquid is directly proportional to the area of contact $(A)$ and the velocity gradient $(\frac{du}{dz})$.
Mathematically,this is expressed as $F \propto A \frac{du}{dz}$.
Introducing the coefficient of viscosity $(\eta)$ as the constant of proportionality,we get $F = \eta A \frac{du}{dz}$.

(C) The viscosity of a liquid generally decreases with an increase in temperature due to the decrease in intermolecular forces.
Surface tension of a liquid also decreases with an increase in temperature because the kinetic energy of molecules increases,reducing the cohesive forces.
However,the effect of impurities on viscosity and surface tension is not uniform.
For example,highly soluble solutes like sugar increase the viscosity of water,while some other impurities may decrease it.
Similarly,surface-active agents (surfactants) decrease the surface tension of water,while inorganic salts increase it.
Therefore,both statements $C$ and $D$ are incorrect as they use the word 'always'.

(B, D) The root mean square velocity is given by $C = \sqrt{\frac{3RT}{M}}$. Since $C \propto \frac{1}{\sqrt{M}}$ and $M_{Y} > M_{X}$,it follows that $C_{X} > C_{Y}$.
The average kinetic energy per molecule of an ideal gas is given by $E = \frac{3}{2} k_{B} T$,where $k_{B}$ is the Boltzmann constant.
Since both gases are at the same temperature $T$,their average kinetic energies per molecule are equal,i.e.,$E_{X} = E_{Y} = \frac{3}{2} k_{B} T$.
Thus,both $C_{X} > C_{Y}$ and $E_{X} = E_{Y} = \frac{3}{2} k_{B} T$ are correct relations.

(C) When two different ideal gases are mixed under isothermal reversible conditions,the process is spontaneous and leads to an increase in the randomness of the system.
The entropy of mixing,$\Delta S_{mix}$,is given by the formula $\Delta S_{mix} = -n R \sum x_i \ln x_i$,where $x_i$ is the mole fraction of each gas.
Since $x_i < 1$,$\ln x_i$ is negative,making $\Delta S_{mix}$ always positive.
Therefore,the entropy of the system increases.