Telangana Board Solutions for Chapter: Kinetic Theory, Exercise 1: EXERCISES

Prove that the average kinetic energy of a molecule of an ideal gas is directly proportional to the absolute temperature of the gas.

Two thermally insulated vessels $1$ and $2$ of volumes $V_1$ and $V_2$ are joined with a valve and filled with air at temperature $\left(T_1, T_2\right)$ and pressures $\left(P_1,P_2\right)$ respectively. If the valve joining the two vessels is opened, what will be the temperature inside the vessels at equilibrium.

What is the ratio of r.m.s speed of Oxygen and Hydrogen molecules at the same temperature?

Four molecules of a gas have speeds $1 \mathrm{km}/\mathrm{s}, 2 \mathrm{km}/\mathrm{s}, 3 \mathrm{km}/\mathrm{s}$ and $4 \mathrm{km}/\mathrm{s}$. Find the rms speed of the gas molecule.

If gas has 'f' degrees of freedom, find the ratio of C_P and C_V.

Calculate the molecular K.E of $1$ gram of Helium (Molecular weight $4$) at $127 °\mathrm{C}$. Given $\mathrm{R}=8.31 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$.

When pressure increases by $2\%$. What is the percentage decrease in the volume of a gas, assuming Boyle's law is obeyed?

Derive an expression for the pressure of an ideal gas in a container from Kinetic theory and hence give Kinetic Interpretation of temperature.