### Related Formula The ratio of specific heats gamma$\gamma$ is related to degrees of freedom f$f$ by: gamma = fracC_PC_V = 1 + frac2f$\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$ ### Core Logic Determine the degrees of freedom $ ### Core Logic Determine the degrees of freedom $f for each type of gas: - **Monoatomic gas**: Translational only $ for each type of gas: - **Monoatomic gas**: Translational only $\implies f = 3 $ $gamma = 1 + frac23 = frac53 quad text(Matches C-I)$\gamma = 1 + \frac{2}{3} = \frac{5}{3} \quad \text{(Matches C-I)}$ - **Diatomic rigid gas**: Translational (3) + Rotational (2) $ - **Diatomic rigid gas**: Translational (3) + Rotational (2) $\implies f = 5 $ $gamma = 1 + frac25 = frac75 quad text(Matches D-II)$\gamma = 1 + \frac{2}{5} = \frac{7}{5} \quad \text{(Matches D-II)}$ ### Step 1: Check Remaining Categories - **Diatomic non-rigid gas**: Translational (3) + Rotational (2) + Vibrational (2) $ ### Step 1: Check Remaining Categories - **Diatomic non-rigid gas**: Translational (3) + Rotational (2) + Vibrational (2) $\implies f = 7 $ $gamma = 1 + frac27 = frac97 quad text(Matches B-IV)$\gamma = 1 + \frac{2}{7} = \frac{9}{7} \quad \text{(Matches B-IV)}$ - **Triatomic rigid gas**: Translational (3) + Rotational (3) $ - **Triatomic rigid gas**: Translational (3) + Rotational (3) $\implies f = 6 $ $gamma = 1 + frac26 = 1 + frac13 = frac43 quad text(Matches A-III)$\gamma = 1 + \frac{2}{6} = 1 + \frac{1}{3} = \frac{4}{3} \quad \text{(Matches A-III)}$ This yields the matching order: A-III, B-IV, C-I, D-II. ### Pattern Recognition Sees: Degrees of freedom and $ This yields the matching order: A-III, B-IV, C-I, D-II. ### Pattern Recognition Sees: Degrees of freedom and $\gamma values. Shortcut: Lower degrees of freedom result in higher $ values. Shortcut: Lower degrees of freedom result in higher $\gamma values. Order of degrees of freedom: Monoatomic (3) < Diatomic rigid (5) < Triatomic rigid (6) < Diatomic non-rigid (7). Corresponding $ values. Order of degrees of freedom: Monoatomic (3) < Diatomic rigid (5) < Triatomic rigid (6) < Diatomic non-rigid (7). Corresponding $\gamma: $: $\frac{5}{3} > \frac{7}{5} > \frac{4}{3} > \frac{9}{7}$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Kinetic Theory

### Related Formula mathrmV_mathrmrms = sqrtfrac3mathrmRmathrmTmathrmM implies mathrmV_mathrmrms^2 = frac3mathrmRmathrmMmathrmT$\mathrm{V}_{\mathrm{rms}} = \sqrt{\frac{3\mathrm{R}\mathrm{T}}{\mathrm{M}}} \implies \mathrm{V}_{\mathrm{rms}}^2 = \frac{3\mathrm{R}}{\mathrm{M}}\mathrm{T}$ ### Core Logic The parameter asked is the mean squared velocity, which corresponds directly to mathrmV_mathrmrms^2$\mathrm{V}_{\mathrm{rms}}^2$. From the ideal gas kinematics relation, we observe: mathrmV_mathrmrms^2 propto mathrmT$\mathrm{V}_{\mathrm{rms}}^2 \propto \mathrm{T}$ Comparing this format against standard geometric linear templates (y = mx$y = mx$), the curve must map as a clean straight line originating from absolute zero zero coordinates. ### Step 1: Final Conclusion This linear profile matches Graph (1), selecting option (1). ### Pattern Recognition Watch the vertical ordinate labels carefully: Root-mean-square velocity scales as a sub-linear curve (sqrtmathrmT$\sqrt{\mathrm{T}}$), while mean squared metric trends linearly directly (y propto x$y \propto x$). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Kinetic Theory

### Related Formula f = frac1T = fracv_textavglambda$f = \frac{1}{T} = \frac{v_{\text{avg}}}{\lambda}$ where: * f$f$ = frequency of collisions * v_textavg$v_{\text{avg}}$ = average speed of the molecules * lambda$\lambda$ = mean free path ### Core Logic Given parameters: * Average speed, v_textavg = 600mathrm~m/s$v_{\text{avg}} = 600\mathrm{~m/s}$ * Mean free path, lambda = 3 times 10^-7mathrm~m$\lambda = 3 \times 10^{-7}\mathrm{~m}$ ### Step 1: Calculate Frequency Substitute the values into the formula: f = frac6003 times 10^-7 = 2 times 10^9mathrm~s^-1$f = \frac{600}{3 \times 10^{-7}} = 2 \times 10^{9}\mathrm{~s}^{-1}$ Hence, the collision frequency is 2 times 10^9/mathrms$2 \times 10^{9}/\mathrm{s}$. ### Pattern Recognition Collision frequency is simply distance covered per unit time (average velocity) divided by the average distance between consecutive collisions (mean free path). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Kinetic Theory