Question
A child has near point at 10cm. What is the maximum angular magnification the child can have with a convex lens of focal length 10cm?
✓
Answer
The child has D = 10cm and f = 10cm. The maximum angular magnification is obtained when the image is formed at near point.$\text{m}=1+\frac{\text{D}}{\text{f}}=1+\frac{10}{10}=1+1=2$
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→- Find the radius of the shadow of the ring formed on the ceiling if r = 15cm.
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Polyatomic Gases: In general a polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number (f) of vibrational modes. According to the law of equipartition of energy, it is easily seen that one mole of such a gas has$ C_v= (3 + f)$ R and $C_p= (4 + f) R$ and $\gamma=\frac{(4 + \text{f})}{(3+\text{f})}$
→For an ideal gas, $C_p - C_v = R$ Where Cp is the molar specific heat at constant pressure. Thus, $\text{C}_\text{P} =(\frac{5}{2})\text{R}$ The ratio of specific heats IS $\gamma=\frac{\text{cp}}{\text{cv}}=\frac{5}{3}$ Diatomic Gases: a diatomic molecule treated as a rigid rotator, like a dumbbell, has 5 degrees of freedom: 3 translational and 2 rotational. Using the law of equipartition of energy, the total internal energy of a mole of such a gas is $\text{U}=\frac{5}{2}\text{RT}$ The molar specific heat at constant volume cv is given by$\text{Cv}=\frac{\text{DU}}{\text{DT}}=(\frac{5}{2})\text{R}$
For an ideal gas, $C_p – C_v= R$ Where Cp is the molar specific heat at constant pressure. Thus, $\text{C}_\text{P} =(\frac{7}{2})\text{R}$ The ratio of specific heats IS $γ( \text{for rigid diatomic)}=\frac{\text{C}_\text{P}}{\text{C}_\text{v}} =(\frac{7}{5})\text{R}$ For non rigid diatomic molecules they have additional mode of vibrations therefore$\gamma=\frac{\text{C}_\text{p}}{\text{C}_\text{v}}=\frac{9}{7}$
Polyatomic Gases: In general a polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number (f) of vibrational modes. According to the law of equipartition of energy, it is easily seen that one mole of such a gas has$ C_v= (3 + f)$ R and $C_p= (4 + f) R$ and $\gamma=\frac{(4 + \text{f})}{(3+\text{f})}$
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- $\frac{5}{3}$
- $\frac{7}{5}$
- $\frac{9}{5}$
- None of these
- For diatomic rigid molecules ratio of specific heats is γ
- $\frac{5}{3}$
- $\frac{7}{5}$
- $\frac{9}{7}$
- None of these
- For diatomic non rigid molecules ratio of specific heats is γ
- $\frac{5}{3}$
- $\frac{7}{5}$
- $\frac{9}{7}$
- None of these
- Give cp and cv values and ratio of specific heat for monatomic gas molecules.
- Give cp and cv values and ratio of specific heat for polyatomic gas molecules
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$\therefore\text{y}=2\text{a}\cos\pi(\text{v}_1-\text{v}_2)\text{t}.\sin\pi(\text{v}_1-\text{v}_2)\text{t}$ is the required equation of beats. Beat frequency is given by $\text{v}_{\text{beat}}=\text{v}_1-\text{v}_2$ Beat period is given by
$\text{T}=\frac{1}{\text{Beat frequency}}=\frac{1}{\text{v}_1-\text{v}_2}$
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$\text{T}=\frac{1}{\text{Beat frequency}}=\frac{1}{\text{v}_1-\text{v}_2}$
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