Q. No.The internal energy of air in \(4~\text m \times 4~\text m \times 3~\text m \) sized room at \(1\) atmospheric pressure will be: (in \(\times 10^6~\text J\)) (Consider air as diatomic molecules)
1. \(12\)
2. \(34 \)
3. \(26 \)
4. \(42\)
1. \(12\)
2. \(34 \)
3. \(26 \)
4. \(42\)
Subtopic: Law of Equipartition of Energy |
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Level 1: 80%+
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The kinetic energy of translation of the molecules in \(50~\text g\) of \(CO_2\) gas at \(17^\circ \text{C}\) is
1. \(4205.5~\text J\)
2. \(3986.3~\text J\)
3. \(4102.8~\text J\)
4. \(3582.7~\text J\)
1. \(4205.5~\text J\)
2. \(3986.3~\text J\)
3. \(4102.8~\text J\)
4. \(3582.7~\text J\)
Subtopic: Law of Equipartition of Energy |
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Level 2: 60%+
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For a diatomic gas, if \(\gamma_1=\left(\dfrac{C_p}{C_v}\right) \) for rigid molecules and \(\gamma_2=\left(\dfrac{C_p}{C_v}\right) \) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct?
(\(C_p\) and \(C_v\) are specific heats of the gas at constant pressure and volume)
1. \(\gamma_2 = \gamma_1\)
2. \(2\gamma_2 = \gamma_1\)
3. \(\gamma_2 < \gamma_1\)
4. \(\gamma_2 > \gamma_1\)
(\(C_p\) and \(C_v\) are specific heats of the gas at constant pressure and volume)
1. \(\gamma_2 = \gamma_1\)
2. \(2\gamma_2 = \gamma_1\)
3. \(\gamma_2 < \gamma_1\)
4. \(\gamma_2 > \gamma_1\)
Subtopic: Law of Equipartition of Energy |
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The translational degrees of freedom \(\left(f_t\right)\) and rotational degrees of freedom \(\left(f_r\right)\) of \(\mathrm{CH}_4\) molecule are:
1. \(f_t=3\) and \(f_r=3\)
2. \(f_t=2\) and \(f_r=3\)
3. \(f_t=2\) and \(f_r=2\)
4. \(f_t=3\) and \(f_r=2\)
1. \(f_t=3\) and \(f_r=3\)
2. \(f_t=2\) and \(f_r=3\)
3. \(f_t=2\) and \(f_r=2\)
4. \(f_t=3\) and \(f_r=2\)
Subtopic: Law of Equipartition of Energy |
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Level 2: 60%+
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Energy of \(10\) non rigid diatomic molecules at temperature T is :
1. \(35\) KBT
2. \(35\) RT
3. \(\frac{7}{2}\) RT
4. \(70\) KBT
Subtopic: Law of Equipartition of Energy |
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In a mixture, \(0.5\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ne}\) gas are taken at temperature \(T\). The internal energy of the system is equal to:
1. \(\left ( \dfrac{13}{2} \right )RT\)
2. \(\left ( \dfrac{11}{4} \right )RT\)
3. \(\left ( \dfrac{29}{4} \right )RT\)
4. \(\left ( \dfrac{13}{4} \right )RT\)
1. \(\left ( \dfrac{13}{2} \right )RT\)
2. \(\left ( \dfrac{11}{4} \right )RT\)
3. \(\left ( \dfrac{29}{4} \right )RT\)
4. \(\left ( \dfrac{13}{4} \right )RT\)
Subtopic: Law of Equipartition of Energy |
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What is the molar-specific heat capacity of a diatomic gas in an isochoric process if it has an additional vibrational mode?
\(\begin{align} & {{1}{.}\;\frac{5}{2}{R}}\\ & {{2}{.}\;\frac{3}{2}{R}}\\ & {{3}{.}\;\frac{7}{2}{R}}\\ & {{4}{.}\;\frac{9}{2}{R}} \end{align} \)
\(\begin{align} & {{1}{.}\;\frac{5}{2}{R}}\\ & {{2}{.}\;\frac{3}{2}{R}}\\ & {{3}{.}\;\frac{7}{2}{R}}\\ & {{4}{.}\;\frac{9}{2}{R}} \end{align} \)
Subtopic: Law of Equipartition of Energy |
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Level 2: 60%+
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The ratio of specific heats \(\left (\dfrac{C_p}{C_v}\right)\) in terms of degree of freedom \((f)\) is given by:
| 1. | \(\left(1+\dfrac{f}{3}\right) \) | 2. | \(\left(1+\dfrac{2}{f}\right)\) |
| 3. | \(\left(1+\dfrac{f}{2}\right) \) | 4. | \(\left(1+\dfrac{1}{f}\right)\) |
Subtopic: Law of Equipartition of Energy |
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Which of the following statements about degrees of freedom are correct?
Choose the correct option from the options given below:
| (A) | A molecule with \(n\) degrees of freedom has \(n^2\) different ways of storing energy. |
| (B) | Each degree of freedom is associated with an average energy of \(\dfrac{1}{2} R T\) per mole. |
| (C) | A monoatomic gas molecule has \(1\) rotational degree of freedom whereas a diatomic molecule has \(2\) rotational degrees of freedom. |
| (D) | \(CH_4\) has a total of \(6\) degrees of freedom. |
Choose the correct option from the options given below:
| 1. | (B) and (C) only |
| 2. | (B) and (D) only |
| 3. | (A) and (B) only |
| 4. | (C) and (D) only |
Subtopic: Law of Equipartition of Energy |
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Level 2: 60%+
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The correct relation between the degrees of freedom \(f\) and the ratio of specific heat \(\gamma\) is:
1. \({f}=\dfrac{2}{\gamma+1}\)
2. \(f=\dfrac{2}{\gamma-1}\)
3. \({f}=\dfrac{1}{\gamma+1}\)
4. \({f}=\dfrac{\gamma+1}{2}\)
1. \({f}=\dfrac{2}{\gamma+1}\)
2. \(f=\dfrac{2}{\gamma-1}\)
3. \({f}=\dfrac{1}{\gamma+1}\)
4. \({f}=\dfrac{\gamma+1}{2}\)
Subtopic: Law of Equipartition of Energy |
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Level 1: 80%+
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